TabStruct: Measuring Structural Fidelity of Tabular Data
Authors: Xiangjian Jiang
Nikola Simidjievski
Mateja Jamnik
Venue: ICLR 2026 Oral (2026)
Keywords: Tabular data
Tabular data structure
Synthetic data generation
Primary area: datasets and benchmarks
TL;DR: We propose TabStruct, a comprehensive benchmark, along with a novel metric, global utility, for evaluating the structural fidelity of tabular data without requiring access to ground-truth causal structures.

Abstract: Evaluating tabular generators remains a challenging problem, as the unique causal structural prior of heterogeneous tabular data does not lend itself to intuitive human inspection. Recent work has introduced structural fidelity as a tabular-specific evaluation dimension to assess whether synthetic data complies with the causal structures of real data. However, existing benchmarks often neglect the interplay between structural fidelity and conventional evaluation dimensions, thus failing to provide a holistic understanding of model performance. Moreover, they are typically limited to toy datasets, as quantifying existing structural fidelity metrics requires access to ground-truth causal structures, which are rarely available for real-world datasets. In this paper, we propose a novel evaluation framework that jointly considers structural fidelity and conventional evaluation dimensions. We introduce a new evaluation metric, global utility, which enables the assessment of structural fidelity even in the absence of ground-truth causal structures. In addition, we present TabStruct, a comprehensive evaluation benchmark offering large-scale quantitative analysis on 13 tabular generators from nine distinct categories, across 29 datasets. Our results demonstrate that global utility provides a task-independent, domain-agnostic lens for tabular generator performance. We release the TabStruct benchmark suite, including all datasets, evaluation pipelines, and raw results. Code is available at https://github.com/SilenceX12138/TabStruct.

Published as a conference paper at ICLR 2026
TABSTRUCT: MEASURING STRUCTURAL FIDELITY OF TABULAR DATA
Xiangjian Jiang', Nikola Simidjievski- Mateja Jamnik'
Deppatment of Computer Science and Technology. University of Cambridge, UK Télécom Paris, Institut Polytechnique de Paris, France
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ABSTRACT
Evaluating tabular generators remains a challenging problem, the unique causal structural prior of heterogeneous tabular data does not lend itself to intuitive human inspection. Recent work has introduced structural fidelity as a tabular-specific evaluation dimension to assess whether synthetic data complies with the causal structures of real data. However, existing benchmarks often neglect the interplay between structural fidelity and conventional evaluation dimensions, thus failing to provide a holistic understanding of model performance. Moreover, they are typically limited to toy datasets, quantifying existing structural fidelity metrics requires access to ground-truth causal structures, which are rarely available for real-world datasets. In this paper, propose novel evaluation framework that jointly considers structural fidelity and conventional evaluation dimensions. We introduce new evaluation metric, global utility, which enables the assessment of structural fidelity even in the absence of ground-truti causal structures. In addition, we present TabStruct, a comprehensive evaluation benchmark offering large-scale quantitative analysis on 13 tabular generators from nine distinct categories, across 29 datasets. Our results demonstrate that global utility provides mesk-independent, domain-agnostic lens for tabular generator performance. We release the TabStruct benchmark suite, including all datasets, evaluation pipelines, and raw results. Code is available
com wgt.taab..cm//iieeeeelllll. TabStruct
INTRODUCTION
Tabular data generation is cornerstone of many real-world machine learning tasks (Borisov et al. 2022: Fang et al. 2024), ranging from training data augmentation (Margeloiu al. 2024 Cui et al. 2024) to missing data imputation (Zhang et al. 2023 Shi al., 2025). These applications underscore the importance of generative modelling, which necessitates appropriate understanding of the underlying data structure (Kingma& & Welling 2014 Goodfellow et al. 2014) Bilodeau et al. 2022).
For instance, textual data conforms to the distributional hypothesis, and thus the autoregressive models are a natural workhorse for the text generation process (Zhao et al. 2023 Sahlgren 2008). In contrast the homogeneous modalities like text, tabular data can pose different structural prior due to its heterogeneity the features within a dataset typically have varying types and semantics, with feature sets that can differ across datasets (Grinsztajn al. 2022 Shi al. 2025). Recent work (Hollmann) et al., 2025) on tabular foundation predictors has empiriclly demonstrated that the Structural Causal Model (SCM) is an effective structural prior of tabular data. As such, it important to investigate how effectively existing tabular generative models capture and leverage the causal structures.
Prior work (Hansen et al. 2023 Qian al. 2024 Du Li 2024 Tu et al. 2024 Livieris et al. 2024
Kapar et al. 2025) has attempted to assess tabular data generators by evaluating the synthetic data they produce. However, the prevailing evaluation paradigms still exhibit three primary limitations, which are summarised in Table (i) Insufficient tabular-specific fidelity assessments. Current benchmarks largely adopt evaluation dimensions from homogeneous data modalities, such as density estimation (Alaa et al.] 2022), machine learning (ML) efficacy (Xu et al.] 2019),, and privacy preserva- tion (Kotelnikov et al. 2023). While effective in other modalities, they exhibit conceptual limitations when applied to tabular data they do not explicitly assess the unique structural prior of tabular

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Figure 1: Illustrative example highlighting the importance of fidelity check for tabular data structure. D: A real-world physical system showing the gravitational forces acting on ball A. The system is described by ball density (p), volume (V), masses (MA & mg), distance (r), and gravitational forces (Fball & FFarh)). For simplicity, we assume both balls share identical density, 2: We derive the ground-truth (GT) causal structure of the system based on Newton's 's law of universal gravitation. 3: We interpret the encoded physical laws of the system as the conditional independence (CI) across variables. 4:: We evaluate four generators by conventional metrics. 3): We assess the structural fidelity by CI tests and the proposed global utility metric. We note that the global structure reflects full conditional independence across all variables, while the local structure includes only those directly relevant to specific prediction task at hand (Foat). Results demonstrate that conventional metrics are insufficient: for instance, while SMOTE is able to outperform other generators on conventionally used dimensions (e.g., ML efficacy)- - the generated synthetic data only preserves local structure and violates most physical laws. For tabular data, where the truthfulness and authenticity of synthetic data is hard to verify, global utility provides effective mechanism for evaluating the alignment of the synthetic data to the likely ground-truth causal structure.
data. A notable example is that many generators (e.g., SMOTH) can produce synthetic data with similar density estimation as real data, yet still violate underlying causal structures such as physical laws illustrated in Figure ()) Although CauTabBench (Tu et al. 2024) takes a step forward to assess the structural fidelity of synthetic data, it remains confined to toy SCM datasets (i.e., synthetic datasets derived from random SCMs), offering limited insight into real-world tabular data, where the ground-truth SCMs are unavailable. (ii) Potential evaluation biases. Many benchmarks (Hansen al. 2023 Qian et al., 2024) and model studies (Xu et al., 2019 Margeloiu al. 2024 Zhang et al. 2023) prioritise MI efficcyy as the principal dimension for assessing generator performance. For instance, a classification setting, generator often considered effective if its synthetic data allows downstream models to achieve high predictive performance. However, while useful, ML efficacy can be highly sensitive to the choice of prediction task and target (Figure 5 and Section (.2).
(iii) Limited evaluation scope. Existing benchmarks mainly consider only narrow range of datasets and generative models (Table []. which restricts their ability to provide a thorough and generalisable comparison of model performance across the broader landscape of tabular generative modelling.
In this paper, we aim to bridge these gaps by introducing a systematic and comprehensive evaluation framework for existing tabular generative models, with particular focus on the structural prior
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29 challenging tabular datasets
13 tabular generative models
4 complementary ovaluation dimansions
Reforence
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9 generator cxtegories les
Iyperpanamate
Density Estiation
Privacy Preseration
ML
Structaral
Fiielty
Classiiaation
Regression
345-100,000 comple
6-145 foatures
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WAF
CAN
Tree
Diffusion
LMM
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Figure 2: Overview of the proposed evaluation framework. TabStruct provides comprehensive evaluation benchmark, including structural fidelity and conventional dimensions, for 13 representative tabular generative models on 29 challenging tabular datasets.
of tabular data. Our proposed framework is characterised by five key concepts: (i) We explicitly incorporate structural fidelity of synthetic data as a core evaluation dimension for tabular generative models. Structural fidelity can directly reflect model capability in learning the structure of tabular data, without biasing towards a specific prediction target. In addition, investigate its interplay with three conventional evaluation dimensions, offering customised guidance for selecting suitable generators across diverse use cases. (ii) We evaluate structural fidelity expert-validated validated SCM datasets. To ensure alignment with ground-truth causal structures, we avoid using toy SCMs and instead select SCM datasets with expert-validated causal structures. With ground-truth SCMs, quantify structural fidelity through h the difference in conditional independence (CI) between real and synthetic data as shown in Figure ()). (iii) We further extend the evaluation of structural fidelity to real-world datasets, where the ground-truth SCMs are unavailable. To this end, we propose a novel evaluation metric, global utility, which treats each variable as a prediction target and measures how well it can be predicted using other variables. Importantly, global utility does not require ground-truth causal structures, thus enabling the evaluation of structural fidelity in real-world scenarios. (iv) We conduct an extensive empirical study on the performance of 13 tabular generators spanning nine categories on 29 datasets, resulting in a total of over 150,00 000 evaluations. The large evaluation scope can ensure holistic and robust benchmarking results. (v) We introduce TabStruct (Figure 2), the benchmark suite developed for this work. This open- source library aims to help the research community explore tabular generative modelling within standardised framework.
Across both SCM and rorl-world datasets, our primary finding is:
Structural fidelity, as quantified by the proposed global utility, should be core dimension when evaluating tabular generative models.
The benchmark results suggest the prevailing paradigm (i.e., optimising tabular generators primar- ily for improved density estimation and ML efficacy) is insufficient. In contrast, our proposed global utility provides insights into crucial yet underexplored perspective tabular-specific fidelity assessments. Our contributions can be summarised as follows:
We propose a unified evaluation framework for tabular generators that integrates structural fidelity with conventional dimensions, and introduce global utility, novel metric that measures structural fidelity without requiring access to ground-truth causal structures. We release the TabStrucr benchmark suite, including datasets, generator implementations, evaluation pipelines, and all raw results.
Conceptual (Section 3p:
Technical (Section 3)
We conduct large-scale quantitative study of 13 tabular generators on 29 datasets. The results offer actionable insights into model performance and can inspire the design of more effective tabular generators by attending to the unique structural prior of tabular data.
Empirical (Section f
2 RELATED WORK
Tabular Generator Benchmarks. An extensive line of benchmarks (Stoian et al.] 2025 Hansen
ct al.) 2023 Qian et al.] 2024 Du & Li 2024 Kindji et al.) 2024 Sidorenko et al. 2025 Long ctt al. 2025) has been proposed for tabular data generation, conventionally established around three dimensions: density estimation, privacy preservation, and ML efficacy. Mainstream evaluation metrics typically capture specific aspects of inter-feature interactions. However, they rarely assess whether the underlying causal structures are preserved in the generated tabular data.
Density estimation (Hansen et al. 2023 Alaa et al. 2022 Shi et al. 2025: Zhang et al. 2023) assesses the divergence between real and synthetic data distributions. However, it fails to explicitly
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Table 1: Evaluation scope comparison between TabStruct and prior tabular generative mod- elling benchmarks. TabStruct presents a comprehensive evaluation framework for tabular generative models, incorporating a wide range of evaluation dimensions, datasets, and generator categories.
Beachmark
Deseiy Eximerin
Conventioaal dimeusonss Prinacy Pracevation
ML. Fificaay
SCM dais Rral-wordd ihep
Structural Bdelits
Duta
Meckle
Generator
3225
X
2034
X
x
SonMete
x
x
7
Liveris et
5
3025
Kapor
Tah (Cars)
13
capture featrreeature causal interactions. ML efficacy (Xu al. 2019 Qian et al. 2024, Seedat iet al. (2024) Tiwald et al. (2225) evaluates the performance difference when real data is replaced with synthetic data in downstream tasks, which primarily focuses on pyy x). thus inherently prioritising feature-target relationships over inter-feature interactions. Privacy preservation (Du &
Li Li, 2024 Kotelnikov et af. 2023 Hu et al. 2024] Espinosa Figueira 2023), although essential in privacy-sensitive scenarios, is generally task-specific and usually does not necessitate high structural fidelity (Chundawat et al. 2022 Livieris et al., 2024 McLachlan et al. 2018). Recent efforts such as Syntheity (Qian al. (024) and SynMeter (Du & Li (024) have aimed to standardise the evaluation of tabular data generators by incorporating the three conventional dimensions. Nonetheless, they omit explicit assessment of tabular data structure. To the best of our knowledge, Cau CauTTaBeenhh (Tu et al.) 2024) is the only other benchmark to explicitly evaluate structural fidelity, but it is limited to toy SCM datasets, existing metrics (Chen et al. 2023a Spirtes al. 200T) typically assume access to the ground-truth SCMs a condition that is seldom satisfied and arguably infeasible for most real-world datasets (Kaddour et al., 2022 Glymour al. 2019] Zhou al. 2024). In addition, some prior studies (Pang et al.) |024 Soolaooro & Dupriez 2023) have attempted to examine relationships across multiple tables within relational database. However, such approaches remain limited in their ability to reflect inter-feature causal interactions within a single table. We further provide detailed summary of prior studies on tabular data generation in Appendix A To bridge these gaps, we introduce TabStruct, unified evaluation framework, along with global utility, an SCM-free metric that quantifies the preservation of causal structures in tabular data.
3 METHODS
3.1 PROBLEM SETUP
Dataset and tabular generator. Let Diun = ((x(), ) ~ p(x represent a labelled tabular dataset with (9) E RR," We refer to the d-th feature (i.e., column/variable) as ad, and the d-th feature of the i-th sample (i.e., a cell) as x For notational simplicity, we define #D+1 == ( LV so that the full collection of variables, including both features and target, can be written as = fI1,.... ......... ID, D+1). }. We denote the training split of Diuli as the reference dataset (Deut), and test data as D Diest A tabular generator is trained on Dier and aims to generate synthetic data Dayn p(x, 7) close p(x, y)- We evaluate the quality of Djer wrt. all the metrics, thus providing benchmark performance against which Dey is compared. We refer to any dataset being assessed as "evaluation dataset D", thus, both Diet and Dayo may serve evaluation datasets.
Structural causal models (SCM). Under the assumptions of causal sufficiency, the Markov property, and faithfulness, an SCM is defined by the quadruple M == (X, G.F.F.FF F)E). G is the causal graph that encodes the causal relationships among the variables. E { D+1 denotes the exogenous noise,
and F = (J, p+1 is the set of structural functions. Each variable æz is determined by function f, of its parents and its exogenous noise, that is, x; ff (pa(æ)) e2), where pa(æ,) S X \ {æy} denotes the parent set of x, in the graph G.
Structural fidelity. As empirically effective structural prior for tabular data, SCM provides formal framework for the underlying generative processes of tabular data (Hollmann et al. 2025 define the struetural fidelity of tabular generator as the alignment
Tu al.) 2024). Therefore, between the SCMs in its synthetic data and the ground tround-truth causal structures. We further discuss the rationales behind using causal structural prior for tabular data in Appendix
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3.2 CONDITIONAL INDEPENDENCE: QUANTIFYING STRUCTURAL FIDELITY WITH SCM
Motivation. We begin by quantifying structural fidelity under the assumption that the ground-truth SCM is available. Following established benchmarks in causal discovery and inference (Spirtes et al. 2001
Kaddour et al. 2022 Tu et al. 2024). we evaluate structural fidelity at the level of the Markoy equivalence class. At this level, causal structures are represented as completed partially directed acyclic graphs (CPDAGs). The SCMs of Pref and san are equivalent if they entail the same set of
conditional independence (CI) statements (see Figure 1 2 & 33) for an illustration).
CI scores at various granularities. Following prior work (Spirtes
2001 Tu et al. 2024 the full set of CI statements implied by the ground-truth truth SCM on Drer is defined as
Cglobal = {ax I zx SJa) S,,8 S \ {x)) u {(x, 1 os (.,Nh S3Nn S (1)
where S3, and f are the d-separation and d-connection sets for (ay, ax.), respectively. For each CI statement, we assess whether it holds in the evaluation dataset D (i.e., Dier or Ssyn) by conducting a CI test at the significance level a = 0.01 via
1, if the CI statement is not rejected on D level o,
La æk Sy Sy,si D) =
(2)
0, otherwise.
To quantify structural fidelity at varying levels of granularity, we define the CI score for any subset of CI statements C S Celobal as:
CI
1 C
E1[ea(e,, 15, 3yx: = 1]
where CI DC)
[0, 1] measures the fidelity of selected CI statements in D, and 1()) denotes the indicator function. A higher CI score indicates that the evaluation dataset more closely aligns with the structure of the ground-truth SCM. Implementation details for the CI scores in Appendix B
Local structure vs. Global structure. We assess structural fidelity at two levels of granularity: local and global. For local structural fidelity, we define the local CI score, CI (Crocat, D), by considering only the CI statements that directly involve the prediction target y of a given dataset and predictive task. Specifically, we compute the local CI score using Equation B with Crecal
(3) for an illustration). Glocal highlights which features are uninformative for predicting y when conditioned on the corresponding d d-separation sets. Therefore, matching the local CI set indicates which features should be ignored when learning pyy x). A higher local CI score suggests the generator faithfully captures the local structure around the target, implying higher utility for downstream predictive tasks (Section 4.2
Sj.D+1) j E [D]]U( A æ 111) j [D]] (see Figure
For global structural fidelity, we define the global CI score as the CI score computed over the full set of CI statements, that is, CI (Cglobat. D). Global CI provides comprehensive assessment of the entire causal structure encoded in the dataset, mitigating potential bias towards any particular variable.
Rationales for CPDAG-level evaluation. Prior studies (Tu et al., 2024 Spirtes et al. 2001) typically evaluate the causal structure alignment at three different levels: skeleton level, Markov equivalence class level, and causal graph level. At the skeleton level, all causal directions are ignored, resulting in a loss of information about the causal relationships between features. For instance, the causal skeleton unable to reflect encoded physical laws shown in Figure I Therefore, we choose not evaluate structural fidelity at the skeleton level due to its inability to capture reliable causal relationships across variables. At the causal graph level, structural fidelity is assessed by comparing the directed acyelic graphs (DAGs) of the reference and synthetic datasets, which requires reliable causal discovery methods as basis. However, current causal discovery methods struggle to recover accurate DAGs from tabular data (Zanga et al. 2022 Kaddour et al., 2022; Nastl & Hardt 2024). Grounding structural fidelity at the DAG level would introduce additional uncertainty on top of results with questionable reliability, making it even harder draw reliable conclusions.
In contrast, CPDAG-level evaluation strikes a good balance between evaluation efficiency and validity. Unlike full DAG constructing via causal discovery, CPDAG-level evaluation does not require the orientation of all edges, making it a more tractable yet still meaningful metric of structural fidelity. This is supported by the fact that Markov equivalent SCMs serve minimal I-MAPs (Agrawal et al.
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2018) of the joint distribution factorisation p(2) = -1 D+1 p(z; pa (z,)). and causal directions can be further removed. In other words, the CPDAG-level evaluation can retain sufficient real-world semantics for practical use cases, such as the physical laws in Figure Therefore, TabStruct evaluates structural fidelity at the CPDAG level. balancing semantic richness with computational feasibility. More details on the rationale for CPDAG-level evaluation are provided in Appendix
3.3 GLOBAL UTILITY: SCM-FREE METRIC FOR GLOBAL STRUCTURAL FIDELITY
Motivation. The CI scores introduced in Section 3.2 require access to a ground-truth SCM to enumerate the CI statements Cgishal- However, for real-world datasets, such an SCM is typically unavailable or even non-identifiable, thereby precluding direct evaluation of structural fidelity. Fol- lowing prior work on tabular foundation models (Hollmann al. 2025], we adopt an "SCM-inspired and real-data-validated" paradigm to address such a limitation. Specifically, we propose global utility as an SCM free metric for global structural fidelity.
Utility per variable. Given an evaluation dataset D, we treat each variable z, E 2 as prediction target. An ensemble of multiple downstream predictors is trained to predict æ; using the remaining variables X' \ { as inputs. following a standard supervised learning setup. The predictive perfor- mance on Dieu is denoted as Perf, (D), measured using balanced accuracy for categorical variables and root mean square error (RMSE) for numerical variables. We define the utility of variable æ, as the relative performance achieved on evaluation data compared to reference data:
if æ is categorical, Perf, (Dier) Perf, (D),
Utility, (D)
Perfy (D) "Perf,, (Dier), if my is numerical.
Utility offers unified perspective for interpreting downstream performance across mixed variable types: Utility, 2 1 indicates that downstream predictors trained on D perform on par with or better than those trained on Dier for predicting æ,, whereas Utility, < 1 implies loss in predictive power. To mitigate the potential bias from a specific downstream predictor, we ensemble nine different predictors with AutoGluon (Erickson al. 2020). Full technical details are in Appendix B
Local utility. We define the utility of the prediction target y, Utility p+1 (D) as local utility, which aligns with the standard metric used to assess the ML efficacy of tabular data generators. The theoretical (Section 3.2) and empirical (Section 4.2p analysis showcases a strong correlation between the local CI score (CI (Creca,, D)) and the local utility (Utility n+ (D)), suggesting that local utility is an effective measurement of the local structure around target
Global utility. Building on the heuristics from local utility and local structure, we further examine the relationship between global utility and global structure. We define the global utility as Global Utility(D) := DFI Σラ= Utility,(D) We hypothesise that aggregating the utility across all features can be strongly correlated with the global CI score (i.e., CI (Cglabat, D)), as global utility is grounded in the observation that a high-fidelity generator should enable accurate conditional prediction of each variable from the others an idea closely tied the Markov blanket in SCMs (Fu) & Desmarais 2010 Gao & Ji 2016). Indeed, our experiments reveal a strong correlation between supporting that global utility serves as an effective and
global CI and global utility (Section practical metric for evaluating global structural fidelity in the absence of ground-truie -ruth SCMs.
Bias mitigation in global utility. contrast to inherently biased local utility, the proposed global utility treats all features fairly. Specifically, we consider predicting each variable associated with different tasks (e.g., binary classification, multi-class classification, regression, etc.). A change the in magnitude in predictive performance can reflect different task difficulties depending target variable and its type (Feurer et al., 2022 Wistuba et al. 2015) Yogatama & Mann 20 4 Grandini et al., 2020). Consequently, absolute performance scores and their variances are not directly comparable across variables, and aggregating these scores may obscure meaningful differences across tasks (Grinsztajn al.] (2022). To address this, global utility follows the standard practice (Feurer cet al. 2022) Grinsztajn et al. (022)) to aggregate normalised utility scores (Equation (4)), providing a more unified perspective on performance across heterogeneous tasks (Section 4.2 and Appendix F.2

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4 EXPERIMENTS
We evaluate 13 tabular generators on 29 datasets by focusing on four research questions:
Validity of Benchmark Framework (Q1, Section 4.1, and Appendix E.1 Can the proposed evaluation framework yield valid evaluation results regarding generator performance?
Validity of Global Utility (Q2, Section 4.2] and Appendix F.22: Can global utility serve as an effective metric for structural fidelity when ground-truth causal structures are unavailable?
Structural Fidelity of Generators (Q3, Section 4.3 and Appendix E.3): Can existing tabular generators accurately capture the data structures across both SCM and real-worle datasets?
Practicability of Global Utility (Q4, Section 4.4 and Appendix E.4): Can global utility provide stable and computationally feasible evaluation results for structural fidelity?
SCM datasets. To reduce the gap between causal structures in SCM and real-world data, select six expert-validated SCM datasets with 7-64 features. All SCM datasets are publicly available from bnlearn (Scutari 201T). Full dataset descriptions are provided in Appendix D
Real-world datasets. We observe that many existing generators achieve near-perfect performance on commonly used benchmark datasets (Shi et al.. 2025 Zhang et al., (023), suggesting that these datasets offer limited discriminative power. To address this, we select 14 classification datasets from the hard TabZilla suite (McElfresh et al. 2024), containing 846-98. 050 samples and 6-145 features. We further select nine challenging regression datasets, containing 345-22,788 784 samples and 6-82 features. Full dataset descriptions are available in Appendix [
Benchmark generators. TabStruct includes 13 existing tabular data generation methods of nine different categories. In addition, we include Drers where the reference data is used directly for evaluation. Full implementation details are in Appendix D.3
Experimental setup. For each dataset of N samples, we perform nested cross- volsddaaii with repeated shuffle, and the details are available in Appendix[DA. Specifically, we first split the dataset into train and test sets (80% train and 20% test), and further split the train set into a training split (Diet) and validation split (90% training and 10% validation). For classification datasets, we perform stratified splitting to preserve the class distribution. We shuffle the dataset to repeat the splitting 10 times, summing up to 10 runs per dataset. All benchmark generators are trained on Dies. and each generator produces a synthetic dataset with N samples. We tune the parameterised generators using Optuna (Akiba et al., (019) to minimise their average validation loss across 10 repeated runs. Each generator is given at most two hours to complete a single repeat. The reported results are averaged by default over 10 repeats. We aggregate results across all SCM or real-world datasets because the findings are consistent across classification and regression tasks (Appendix E.2). Specifically, we use the average distance the minimum (ADTM) metric via affine renormalisation between the cop-performing and worse- worse-performing models (Grinsztajn et al. 2022 McElfresh et al. 2024 Hollmann et al. 2025 Margeloiu et al. 2024, Jiang et al. 2024). We further provide the detailed configurations (Appendix D and raw results (Appendix
4.1 VALIDITY OF BENCHMARK FRAMEWORK (Q1)
The benchmark results effectively evaluate data quality. demonstrates that all metrics effectively distinguish between high- and low-quality data. Specifically, except for privacy-related metrics, the reference data (Deet) consistently achieves the highest scores. This is expected, as Dief is the ground truth and should score highly on metrics of density estimation, ML efficacy, and structural fidelity. In contrast, privacy metrics reward greater differences from the ground truth to indicate stronger privacy preservation. Since Peer is identical the ground truth, naturally scores poorly for privacy. These results show that the selected metrics provide appropriate evaluations for data quality. Therefore, we consider the evaluation results to be valid and meaningful for analysis.
Structural fidelity is complementary to conventional evaluation dimensions, rather than inter- changeable. On SCM datasets, Figure 3 (left) shows that none of the existing evaluation metrics exhibits a strong correlation with global CI. Notably, SMOTE and BN tend to outperform other models by a clear margin in density estimation. However, their performance degrades greatly when it comes to capturing the global structure of tabular data, as reflected by global CI, consistent with our motivating example in Figure T This discrepancy reveals the limitations of conventional evaluation dimensions and underscores the need to incorporate structural fidelity for inter-feature causal structures.
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Table 2: Benchmark results of 13 tabular generators on 29 datasets. We report the normalised mean + std metric values across datasets. "N/A" denotes that specific metric is not applicable. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CT". The results show that the Top-3 methods in Global CI and Global utility are largely consistent between SCM and real-world datasets. This alignment suggests that the selected SCM datasets represent real-world causal structure, and global utility can serve as an effective metric for global structural fidelity when ground -ruth SCM is unavailable.
Generator
Shape1
Trend o precision
Density Estimation
recall 1
DCR
Preservation
5-Presence
MI. Rfficaey
unlltyy
Local C
Strnetural Fiddlty Global CI
Global unility
SCM datasets
Pit
3000:130
1.00sue
g000gua
1.00s00
0.00guue
0.00
0.99
0.89
1.00gase
4.99
SMOTE
400
anee
0.01
0.92
0.82-312
0.30
0. 0.39
0.80
0.73aum
0.78
0.32
a.65
0.23
0.35
2.49:
TYAE
0.59_419 10
2.6
0.36
0,70
0.13gn11
0.78
0.50
0,40
0.70
GOGGLE
0.46-133 36
0,50
0.87a0a)
0 0.36
a,55
0.38
0.53
0,42=327
0,14-229
0.24-22ss
CTGAN
0.46
0.50
0.7
0 14440e
0.52.mm
0.19asu
0 2.00
0.61 201s
0.08-a14
0. 0.26-22-2
NElow
0,31
0.26
0.31
0. 0.15
0,73
0.51
0.10 0.102006
0.09_300
0.09_a10
0.1 0.122
ARF
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0.35
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0.62-g11
0.60zuz
0.64
0.39
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0.34
0.29aue
0:17=32s
0.69-axs
2.80
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0.50 19
0,48au
0,50
2.32
0.76aum
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0. 0.76
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0.69
0.62
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033
0,50
0.13
0.50
0.58
0.57
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0.67
0.57
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4.00
0.55
0.14
0.59
0,50
0.26
0, p.30
NRGBoust
0.65
50
0.61
0 162mm
0,53
0.28a121
0.75aum
0.64-215
0. 0..66
GRaaT
0.62 34
g.59
0.62
0.38
2.52
0.18
0.27
0,17
0.16
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Real-world datasets
DRr
1.00_430
1.00gmm
g,00
1 1.00g00
0.00
0.00
0.96
N/A
N/A
g.99
SMOTE
0.87
g.11
0.77 10m
1.19
a.02
a.9
N/A
NIA
0.41
BN
0.66-111
0.72xce
0.66am
4.30
0.48
0.07 ssum
0.38
N/A
NIA
0.44,223
TVAE
0,55
18480
0.68210
0.29
0.70guu
N/A
2.53
GOGGLE
0,47
0,57am
0.36
0.50
0.4
0.21 2b10
CTGAN
0.29
0.53umm
0.66
0.11
0.51ana
0.30
0.70
N/A
NIA
0.13
NElow
0,38
0.28amte
0.52ea1s
0.00
0.42amzz
0.10a0ee
N/A
NIA
0.144
ARF
0.58aat
0 021
0.48
2.05
0.542um
N/A
NIA
0.56.2511
TANDDPM
0.43_41
0.49
0.54gmm
0.42
027
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N/A
N/A
0.72
TabSyn
0.44
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0,5
0.24
0.76
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0.73
TabDill
0,51-1
0.52aate
0.69
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0,57
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N/A
N/A
0.734b0
TabEBM
1559_415
0.65
0.79
0.30
0.58
0.14
0.63
N/A
N/A
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2.49
0.622116
2.00m
0,5
0:22
0.342mm
N/A
N/A
0.16
GReaT
0:47,430
0,57,014
0 000
0,52
027
0.23
NIA
N/A
0,20
4.2 VALIDITY OF GLOBAL UTILITY (Q2)
Global utility serves as an effective metric for global structural fidelity. Table and and Figure (left) demonstrate a strong monotonic correlation between global utility and global CI scores (r,- = 0.84, 0.001). To ensure the generalisability of global utility, we extend our evaluation scope, incorporating more complex SCM datasets (Appendix E.2). a wider range of existing metries (Appendix(E.2) and additional downstream tasks (Appendix E..).. Across all settings, global utility consistently exhibits a substantially stronger correlation with global CI than any other metric. Appendix E.22 further shows that global utility more closely aligns with global CI in the induced generator rankings. We would like to emphasise that the high correlation between global CI and global utility is an empirical finding rather than a formal proof of connection between the two metrics. This observation primarily aims offer users actionable and empirically grounded insights into tabular data generation. The strong correlation and consistent generator ranking suggest that global utility offers robust, SCM-fre approach for assessing global structural fidelity.
Local utility is not always the golden standard, due to its bias towards the local structure. We further examine the correlation between local utility and local CI, which only considers the local structure associated with the prediction target. As shown in Figure [3 (left), local utility exhibits a strong correlation with local CI (r. 0.78. p < 0.001). but a much weaker correlation with global CI (r, = 0.14, p < 0.001). The results indicate that local utility may overlook the holistic data structure, while global utility provides a more comprehensive evaluation of structural fidelity.
4.3 STRUCTURAL FIDELITY OF GENERATORS (Q3)
Structure learning methods struggle with tabular data generation. One surprising finding is that BN and GOGGLE do not demonstrate strong performance in structural fidelity, despite their inductive bias towards learning tabular data structures. This observation aligns with prior work (Tu jet al., 2024; Zeng et al., 2022), which highlights that current causal discovery algorithms often struggle when the number of features exceeds 10 - our benchmark datasets have features from 6
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1.0
Local utility 0.63 0.70 0.49
0.62
-.2-0.75-0.37
1.00
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Reference data
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TVAR SMOTE
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TaLEBM
Global utility 0.59 0.75 0.51 0.63 003--00250.66000
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GReaT
GOGGLE
NRGBoost
Shape Trend
at a-precision
B B-recall
DCR
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Local utility Local CI
Global CI
Global utility
NFlow
CTGAN
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Figure 3: Left: Spearman's rank correlation heatmap based on metric values on six SCM datasets. Global utility correlates strongly with global CL, suggesting that global utility can effectively assess global structural fidelity without resorting to SCMs. Right: Mean normalised local utility vs. mean normalised global utility on 23 real-world datasets. SMOTE prioritises local utility, whereas TabDiff and TabSyn generally achieve balanced preservation of both global and local data structures.
up to 145. Furthermore, GOGGLE exhibits notable performance degradation when prior knowledge about the data structure is missing (Liu et al.) 2023). The results underscore the limitations of existing causal discovery methods in recovering precise causal structures from real-world data, further justifying our evaluation the CPDAG level.
Diffusion models generally capture the global structure well. As reported in Table and Figure (right), diffusion-basee models consistently achieve the highest scores global structural fidelity: the Top-3 methods are TabDDPM, TabSyn, and TabDiff across both SCM and real-world datasets. We attribute their strong performance to the inherent learning principle of diffusion models for learning permutation-invarian conditional distributions of each feature. At the training stage, since noise added independently to each feature, the diffusion network is optimised at every denoising step to reconstruct each feature simultaneously by conditioning on others. For instance, TabDDPM and TabDiff implement this principle within each feature type, and TabSyn applies it across all features. Moreover, diffusion models impose no ordering of features. This results in efficient computation (Figure 4 and permutation-invariaaen conditional distributions, a property that aligns naturally with the structure of tabular data. These theoretical properties align with the conditional independence analysis in Section 3.2 thus confirming that diffusion models are capable of capturing global structure.
Language models remain limited in learning tabular data structure. Table shows that the autoregressive model GReaT, even with the help of large language models, fails to outperform even the simple baselines like SMOTE and TVAE. Although token-wise likelihood training is well-established approach for sequential modalities like text and time series, its underlying assump- tions misalign with the permutation -nnvariiinnn nature of tabular data. autoregressive generator needs to linearise the feature set and then factorise the joint distribution as I[ p(X*()) x=(<))), where π denotes a chosen ordering of features. Any fixed ordering т can introduce directional bias. For instance, the bias could harm the estimation of p(z, X' {xr,) }) when appears early in the sequence. While GReaT attempts to mitigate this issue by randomising т when fine-tume tuning large language models, randomising does not resolve the fundamental misalignment and can constrain the performance of autoregressive tabular generators (Appendix E.3
4.4 PRACTICABILITY GLOBAL UTILITY (Q4)
Global utility is robust and stable. Appendix B.2 and Appendix E.4 show that global utility yields stable generator rankings across both nine tuned predictors ("Full-tuned")) and three untuned ones ("Tiny-default"). In contrast, local utility necessitates nine tuned predictors ("Full-tuned") for reliable results. These findings align with the conceptual design of the utility metrics. We note that local utility focuses mainly on the predictive performance of a single target variable, making it susceptible to feature-specife bias, which results in unstable generator rankings across different predictor configurations. In contrast, global utility aggregates performance across all variables, thereby mitigating feature-specific effects and enhancing robustness.

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Normalised global utility"
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Figure 4: Computation efficiency on 23 real-world datasets. Left: Median training time per 1,000 samples mean normalised global utility. Middle: mean normalised global utility. We exclude the outliers (TabEBM and GReaT) due to their long generation time (over 30s). Right: Median evaluation time. Because global utility yields stable generator rankings across downstream predictors ( (Appendix E.4). computing global utility can be highly efficient with only small ensemble of predictors (i.e.. Tiny-default.
Median generation time per 1,000 samples vs.
Global utility provides efficient evaluations of structural fidelity. In practice, interested in identifying the most promising model before fine-tuning it for optimal performance. Global utility supports this by reducing both the tuning burden and the dependency on the number of predictors, while still yielding stable and informative rankings. As illustrated in Figure 4 (right), computing global utility with "Tiny-default" takes only 0.64s per 1000 samples, while local utility requires nearly double the time ("Full-tuned" with 1.21s) for comparable reliability.
often
Limitations and future work. While our proposed global utility is robust and effective metric for assessing global structural fidelity, it is an empirical measurement of the likely SCMs behind the data hand. However, developing a theoretically provable structural fidelity metric for real-world tabular data is highly challenging, as ground-truth causal structures are rarely available, even precluding the possibility theoretical validation. This in line with several open challenges in the field particularly the lack of causal discovery methods that reliably infer the governing SCMs of real-world tabular datasets (Kaddour et al. 2022 Tu et al., 2024 Glymour et al., 2019) Nastl & Hardi 2024). Despite substantial research efforts, recent work (Nastl & Hardt 2024) shows that state-of-the-art causal discovery methods often perform poorly on real-world data and may mislead users. Therefore, we propose global utility primarily as an empirical lens for evaluating tabular data structures. Bridging the gap between theoretical assumptions and real-world causal structures will require advances in causal modelling. As TabStruct library freely available, its development will be an ongoing, community-driver endeavour. Therefore, TabStruct will continue to evolve with advances in causal modelling. We believe that the open-source source nature of TabStruct will help drive progress in theoretical foundations for real-world tabular data challenges. More discussion on future work is in appendix F.5 and Appendix F.6
5 CONCLUSION
We present TabStruct, a principled benchmark for tabular data generators along with both structural fidelity and conventional dimensions. To address the challenge of assessing structural fidelity in the absence of ground-trute SCMs, we introduce global utility a novel, SCM-free metric that enables unbiased and holistic evaluation for tabular data structure.
In our large-scale study of 13 generators across 29 datasets, we find that existing evaluation methods often favour models that capture local causal interactions while neglecting global structure. Our results show that the four evaluation dimensions are complementary, offering practical guidance for selecting suitable generators across diverse applications. We further observe that diffusion models, due to their permutaaiooninnvarian generation process, offer valuable insights into the fundamental representation learning of tabular data. TabStruct is an ongoing effort. As such, it will continue to evolve with additional datasets, generators, and evaluation metrics both through engagement and contributions from the community. We envision that the source nature of TabStruct will help drive progress in high-fidelity tabular generative modelling.
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ETHICS STATEMENT
This paper proposes integrating structural fidelity as a core evaluation dimension alongside conven- tional metrics for assessing tabular data generators. Specifically,, we introduce global utility, novel metric that evaluates the structural fidelity of synthetic tabular data without requiring access to the ground-trutt causal structures. Furthermore, we present TabStruct, a comprehensive benchmark for tabular data generation that spans wide evaluation scope comprising 13 generators from nine distinct categories, evaluated on 29 datasets. Our benchmark results highlight that structural fidelity is an important yet previously underexplored evaluation dimension. It effectively captures whether generated data preserves the underlying causal structures present in real-world tabular datasets, serving as a valuable complement to existing evaluation dimensions.
This is particularly critical for tabular modalities, where visual inspection of data authenticity not feasible, unlike in text image domains (Van Breugel & Van Der Schaar 2024 Zhao et al.) 2023).
By providing a unified benchmark that incorporates both conventional metrics and structural fidelity, TabStruct has the potential foster more reliable and transparent development of generative models.
This can benefit multiple domains that rely on tabular data, such as healthcare (Jiang et al. 2024
Bespalov al. 2016 Morford al. 2011) and scientific research (Margeloiu al., 2022). where
understanding the structural fidelity of generated data is crucial.
The impact of our work extends enabling broader machine learning applications in data-scarce domains. For instance, it can facilitate robust data analysis in clinical contexts where data collection is limited (Margeloiu et al. 2024 Chawla al., 2002 McLachlan et al., 2018). Enhancing the fidelity of synthetic data may promote the adoption of more advanced machine learning approaches. TabStruct could further facilitate safer data sharing
contexts (Jordon et al., 2018 Hu et al.,
2024| (Stoian et al.] [2025] Alami et al. 2020 CCecierski-Holmes et al. (022). support reproducible research through synthetic benchmarks, and broaden access to machine learning capabilities in low-resource data-scarce scenarios.
REPRODUCIBILIIY STATEMENT
Our study is conducted entirely within reproducible setting. As detailed in Appendix [D] all bench- mark datasets are publicly available and widely adopted in the machine learning literature (McElfres) al. 2024 Scutari 2011). We do not use, include, or release any newly collected proprietary data. In addition, the employed tabular generative models and benchmark metrics are not tailored to any specific demographic or sonsii--ensitive dataset. Full implementation details are avail- able in Appendix and the associated codebase (https: : //github com/ /innsSiin SilenceX12138/ TabStruct). Furthermode, we release TabStruct as an open-source library to support transparency, reproducibility, and further community- -rriueeety- development. We welcome community contributions that prioritise safety, fairness, and inclusivity in the future evolution of the benchmark.
ACKNOWLEDGEMENTS
The authors would like to express their gratitude to Prof. Carl Henrik Ek for insightful discussions on structure learning, and to Prof. Ferenc Huszár and Dr. Ruibo Tu for their enlightening perspectives causal machine learning, and to Dr. Andrei Margeloiu for his thoughtful feedback during the early stages of the project. XJ acknowledges the generous support of the Google PhD Fellowship. MJ and NS acknowledge the support of the U.S. Army Medical Research and Development Command of the Department Defense; through the FY22 Breast Cancer Research Program of the Congression- ally Directed Medical Research Programs, Clinical Research Extension Award GRANTI3 MANT13769713 13. Opinions, interpretations, conclusions, and recommendations are those of the authors and are not necessarily endorsed by the Department of Defense.
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Appendix
TabStruct: Measuring Structural Fidelity of Tabular Data
Table of Contents
Summary of Related Work
20
Conventional Evaluation Dimensions
20
A.2 Structural Fidelity of Tabular Data
21
A.3
Tabular Data Genertor)
21
A.4
Evaluation Scope Comparison
21
B
Designs of Structural Fidelity Metries
25
B.I
Conditional Independence (CI) Scores
................................
25
B.1.1
Deriving CT Statements from Causal Graph
................................
25
B.1.2 Compute CI Scores on Tabular Data
25
B.2
Global UGlity Score
25
B.2.1 Downstream Predictor Configurations
25
B.2.2
Pruning the Ensemble of Downstream Predictors
26
Rationales for Evaluation Framework Design
28
Structural Prior for Tabular Data
28
C.2
CPDAG-level Evaluation of Structural Fidelity
28
D Reproducibility
30
D.
Benchmark Datasets
30
D.I.I SCM Datasets
30
D.1.2
Real-world Dalasets
................................
................................
30
D.2
Data Processing
................................
32
D.3
Implementations Benchmark Generators
................................
32
D.4
Hyperparameter Tuning for Downstream Predictors
................................
37
D.5
Aggregation of Evaluation Results)
37
D.6
Software and Computing Resources
37
Extended Analysis and Discussion
38
E.1
Extended Analysis on Validity Benchmark Framework
................................
Extended Analysis on Validity Global Utility
................................
38
E.3
Extended Analysis Structural Fidelity of Generators
42
E,4
Extended Analysis on Practicability of Global Utility
44
E.5
Practical Guidance
47
E.6
Future Work
47
Extended Experimental Results
Evaluation Results SCM Datasels
49
F.I.I
Classification Datasets
49
F.1.2
Regression Datasets
51
F2
Evaluation Results for Real-world Datasets
52
F2.1
Classification Datasets
52
F22.2
Regression Datasets
59
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A SUMMARY OF RELATED WORK
we provide detailed summary of related work on tabular data generation. We begin by outlining the conventional evaluation dimensions for tabular generators (Appendix (.I)). We then highlight the importance of assessing structural fidelity in the evaluation of such models (Appendix A.2). We further summarise existing tabular data generators (Appendix [A.3]. Finally, we present a comprehensive and quantitative comparison of the evaluation scope covered by TabStruct versus prior work, including both benchmarks and model studies (Appendix (A.4).
As a supplement to Section 2
A.1 CONVENTIONAL. EVALUATION DIMENSIONS
Density estimation assesses the discrepancy between the distributions of reference and synthetic data, considering both marginal (i.e.. low-order) and joint (i.e.. high-order) distributions (Hansen et al. 2023; Kim et al. 2023 McCarter 2024 Solatorio & Dupriez 2023 Pang et al., 2024). A generator may achieve high performance on low-order metrics by sampling each feature independently. thereby ignoring inter-feature dependencies. While high-order metrics aim to measure sample-level similarity, they still fall short of explicitly revealing whether the synthetic data preserves the underlying causal structures present in the reference data.
Following prior studies (Hansen et al. 2023 Shi et al. 2025 Zhang et al. 2023). we evaluate density estimation using four metrics of two categories: (i) Low-order: Shape and Trend (Wüst 2011). Shape measures the synthetic data's 's ability to replicate each column's 's marginal density. Trend assesses its capacity to capture correlations between different columns. (ii) High-order: a-precision and 3-recall (Alaa et al. 2022). a-precision quantifies the similarity between the reference and synthetic data, and B-recall assesses the diversity of the synthetic data.
Privacy preservation evaluates the trade-off between the utility of synthetic data in downstream tasks and the risk of privacy leakage (Margeloiu et al. [024 Gulati & Roysdon 2023 Truda 2023
Jordon et al.] 2018 (Zhang et al.] 2021] McKenna et al. 2021 (019)). However, this dimension is often tailored to specific tasks (c.g., classification and regression), and as such, it does not directly evaluate the structural fidelity of tabular data. Consequently, privacy preservation alone cannot comprehensively assess generator's ability to capture the fundamental characteristics of tabular data, such as causal structures.
Following prior studies (Margeloiu al., 2024: Kotelnikov et al., 2023 Zhao al.) 2021 we
measure privacy preservation using two metrics: (i median Distance to Closes! Record (DCR) (Zhao al. 202T), where a higher DCR indicates that synthetic data is less likely to be directly copied from the reference data; (ii) ö-Presence (Qian et al. 2024). We note that some implementations of 8-Presence interpret smaller values as indicative of better privacy preservation; however, we adapt the implementation provided by Synthcity (Qian et al. 2024), wherein larger values correspond to improved privacy preservation. Furthermore, we note that Synthcity implementation can exhibit instability due to inherent numerical issues.
ML efficacy measures the performance gap observed when replacing reference data with synthetic data in downstream tasks. This metric is inherently task-specific and can be heavily biased by the choice of predictive models and target variables. A useful parallel can be drawn from image generation: Mixup (Psaroudakis & Kollias (022)) enhances training data by interpolating between real samples, often improving downstream task performance. However, it simultaneously distorts the spatial structure of images. producing visually unrealistic outputs (Mumuni & Mumuni 2022). As illustrated in Figure I assessing the authenticity of synthetic tabular data is far more difficult than in image domains. Consequently, synthetic data that performs well in downstream tasks may still fail to preserve important causal structures of the reference data. This example shows that MI. efficacy, while useful for specific tasks, cannot serve as holistic measure of a tabular data generator.
Following prior studies (Xu et al., 2019 Margeloiu et al. 2024, (Seedat et al. 2024), we adopt the -yyyttio--syntheticc, test-on-real" strategy for quantifying ML efficacy of synthetic data. To mitigate the bias from downstream models, we evaluate the utility with the performance of an ensemble of nine predictors (i.e., AutoGluon- full (Erickson et al. (020) and TabPFN (Hollmann et al. (025
Specifically, the downstream models include three standard baselines: Logistic Regression (LR) (Cox. 1958). KNN (Fix. (985) and MLP (Gorishniy et al.) 202I): five tree-based methods: Random
Forest (RF) (Breiman 200T), Extra Trees (Erickson et al.) 2020), LightGBM (Ke et al. 2017).
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CatBoost (Prokhorenkova et al. 2018). and XGBoost (Chen & Guestrin 2016); and a PFN method: TabPFN (Hollmann et al. 2025
Furthermore, noted in prior work (Kotelnikov et al.) 2023), tuning downstream models does affect the relative rankings of tabular generators under ML efficacy. Therefore, to draw generalisable conclusions, we perform hyperparameter tuning for all nine predictors, and the technical details are provided in Appendix
A.2 STRUCTURAL FIDELITY OF TABULAR DATA
As illustrated in Figure one of the key desiderata for faithful synthetic tabular data is the preservation of causal structures present in real data. Prior work (Tu et al., 2024) primarily assesses structural fidelity using toy datasets, as existing metrics (Chen et al.) 2023at SSpirees et al.] 2001 typically assume access to the ground-truth SCMs condition that is seldom satisfied and arguably
infeasible for most real-world datasets (Kaddour et al. 2022 Glymour et al. 2019: Zhou et al. 2024
Nastl & Hardi 2024).
To bridge this gap, we introduce global utility, an SCM-free metric that quantifies how well a generator preserves the causal structure of real data. Global utility provides complementary perspective to conventional metrics, enabling more holistic assessment of synthetic tabular data.
A.3 TABULAR DATA GENERTOR
The common paradigm for tabular data generation is to adapt Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs) (Xu et al. 2019). For instance, TableGAN (Park et al.
2018) employs a convolutional neural network to optimise the label quality, and TVAE (Xu et al.
2019) is variant of VAE for tabular data. However, these methods learn the joint distribution and
thus cannot preserve the stratification of the reference data (Margeloiu et al.) 22224). CTGAN (Xu al. 2019) refines the generation be class-conditional. The recent ARF (Watson et al. 2023 an
adversarial variant of random forest for density estimation, and GOGGLE (Liu et al.] 2023) enhances
VAE by learning relational structure with Graph Neural Network (GNN). Another emerging direction is the use of denoising diffusion models (Kotelnikov al. 2023 Zhang et al., 2023 Shi jet al. 2025). For instance, TabDDPM (Kotelnikov et al.] 2023) demonstrates that diffusion models approximate typical distributions of tabular data. In addition, several energy-baset models have recently been proposed for tabular data generation, such as TabEBM (Margeloiu et al., (024) and NRGBoost (Bravo 2025). These models aim improve synthetic data quality by learning energy-based representations of the data distribution.
In a broader context, there is growing interest in adapting Large Language Models (LLMs) for tabular data generation (Fang et al.) 2024 Seedat et al. 2024 Borisov et al., 2023). For example, GReaT fine-tunes GPT-2 generate realistic tabular data, while CLLM leverages the domain knowledge embedded in LLMs during generation. However, most state-of-the-art L.MSs do not disclose their pretraining data, raising concerns about data contamination i.c. whether the reference data (even the test data) has been included during pretraining (Fang et al. [2024] Margeloiu et al. 2024). which can undermine fair comparisons between tabular generators. To ensure fairness and reproducibility. TabStruct excludes models based on proprietary or undisclosed LLMs, such as GPT- 4 Seedat et al. (024)). We restrict our evaluation to models built on fully open-source LLMs, such as GReaT, thereby mitigating concerns related to data contamination. We would like to emphasise that, although TabStruct excludes certain LLM-based tabular generators to ensure fair and uncontaminated benchmarking. researchers and practitioners encouraged to integrate their own LLM-based models.
We acknowledge that some models exist beyond those currently implemented in TabStruct. We note that TabStruct offers unified APIs that support up to nine distinct categories of tabular generators (one of the widest scopes to date shown in Table 4). enabling broad compatibility for most tabular generators. Therefore, beyond its current evaluation scope, TabStruct functions standardised and extensible benchmarking framework. It is designed to accommodate future methods, promoting continued development and evaluation within consistent and reproducible environment.
A.4 EVALUATION SCOPE COMPARISON
Table and Table pressnnt comparative analysis of TabStruct against prior studies the evaluation of tabular generative models. TabStruct considers four key evaluation dimensions: density estimation, privacy preservation, MI. efficacy, and structural fidelity. In addition, it supports all nine categories of
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tabular generators, offering comprehensive and holistic overview of the current landscape of generative modelling for tabular data.
While we acknowledge that the Cau TabBench framework is, in principle, scalable to datasets with higher dimensions than those reported in its original study, we emphasise that the specific causal discovery methods it employs may not be practically scalable in real-world scenarios. For instance, prior work (Zanga et al. 2022) has highlighted the substantial computational overhead associated with causal discovery algorithms such PC. Empirically, we observe that the vanilla PC algorithm used in CauTabBeench may require to 168 hours (i.e., days) to process datasets with more than 50 features. Consequently, several metries within CauTabBench may be computationally infeasible for the real-world datasets considered in TabStruct, suggesting that CauTabBench would require additional technical optimisation for practical deployment. Moreover, recent studies (Nasti Hardt 2024, Zanga et al., (002)) have shown that even state-of-the-an causal discovery methods often perform unreliably on real-world data, potentially leading to misleading conclusions. We also observe such pitfalls of existing causal discovery methods in the considered datasets (Appendix E.2). Thus, applying CauTabBench practice presents challenges not only in terms of scalability but also in reliability. In contrast, TabStruct offers novel and practical contribution by providing SCM-free lens through which to assess causal structures in tabular data.
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# Festtrre minge
Table 3: Comparison considered tabular datasets between TabStruct and prior studies. TabStruct introduces a nove benchmark designed for the holistic evaluation of tabular generative models, with particular emphasis on evaluating the underlying structure of tabular data. It offers diverse suite of datasets spanning both classification and regression tasks, thereby supporting comprehensive and structure-awwer aware evaluation across varied use cases.
48-48
X
X
X
888
12-48
8-51
6:21
12-48
X
8-9
12-48
X
x
7.60
X
6.82
Sample range
39.644-39 04443996644
19,044-39,60 39,44494444
20, 20,640 20.00-20.4400
39, 39,644-13.82 3.824
1.398 1.398-197,668 197 97,080
740 740- 1,036
39,644-13884
835-9,1466
39,044445,824
1,338 19,644
345- 345-100,,000 (000
Regression
X
X
X
X
Mixed feattres
X
X
X
X
X
X
X
X
# Datasets
X
X
X
6
X
X
x
X
X
X
X
12
Unkunwn (private data)
A Claass range
2-7
2-7
2-7
23
2-7
24
2-7
2-2
2:26
2-7
2-3
2-
X
2.7
X
3-5
2-3
2-100
# Feature range
14-54
12-168
6-47
9-57
8.50
10:28
11-25
12:29
7-77
12-50
7-26
X
11:31
18-24
28-28
1.15
6-145
Classtfcatiinn
Sample range
48 08.842-4,0000000 4,000,000
48, 0..84--4.000 4,000,000
110L065-220 0.075 259
48 8-2-842-- 4,000.000
500 -8 1.012
955- 10), 7666
1,473-284.88 307
768- 130,064
1,000 45.211
12,330-8. 1330-888842
10,000- 1161116.22222
Benchmarks
7608-71 71 1,0000
1.941 48,842
5,456-20.757
1,385- 1,385
12,960 48.842
100,000
20-200
20 -00000
10
X
Mode
Mixed features
Unknown
Datanets
10
12
X
8
2
17
Structural Fidelity
X
X
X
NeurlPS 2019
NeurIPS 2019
AISTATS 2023
ICLR 2023
ICLR 2023
ICLR 2023
ICMI 2023
ICML 2023
ICLR 2024
ICMI 2014
NeuriPS 2024
ICLR 2025 2025
ICLR 2025
NeurIPS 2023
NeurIPS 2023
IFTP 2024
DMKD 2025 arXiiv
ICLR 2026
Venue
arXiv
arXivv
NeariPS
TahDDPMM Keee Kecelnikn Imikon ot ml. 2023
2024
Synchheen mutru at.. 2025
NFLDW Dark 2019
Ca Bench Te al. 2024
CTGAN Ku st 2019
DUES
GOGGLE Linaal 2023
2023
STasy Kim et 2003
2123
CLIM Soalun cn 2024
TabEBM Murvellnee al
NRGBBOO Beas 20PA
TabDii al. 200
Syyncoiry On cta 2024
Mente Do & L 2004
CaDi Lewer 2013
TabSyn Zhane of
2023
2004
2025
TabStruck (Oars)
TVAE Xa
GReaT Barbson
Livieris L
Kapar et al
Paper
Humsen
ARt
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Language Model
Table 4: Comparison of considered tabular generative models between TabStruct and prior studies. TabStruct encompassen nine distinct categories of tabular generators, enabling comprehensive and systematic comparison across a broad spectrum of generative approaches,
X*
EBM
x
X
X
X
X
Diffusion
x
X X
X
X
V
Tree
X
X
X
*
X
X
X
V
Normalising Flows
Tabu lar Generative Models
3
*
X
X
VAE
X
A
GAN
Bayesian Network
Model studies
Benchmarks
X
X
X
X X X X X X X
X X
X
X
X
# Generators Interpolation
x
X
X
X
X
X
X
X
X
X
7
10
13
NeurlPS 2019
NeurIPS 2019
NeurTPS 2019
AISTATS 2023
ICLR 2023
ICLR 2023
ICLR 2023
ICML 2023
ICML 2023
ICLR 2024
ICML 2024
NeurlPS 2024
ICLR 2025
ICLR 2025
NeurlPS 2023
NeurlPS 2023
IHPP 2024
DMKD 2025
ICLR 2026
Venue
arXiv arXiv
arXiv
TabDDPM Kotelnikon nikov etall 2023
2024
SynthE val Lautrup et 20255
NFLOW Durkan et al 2019
CauTabBench To et al, 2024
CTGAN eu al. 2019)
ARF Watson et ul. 2023
GOGGLE [Liu et 2023
GReaT Borissv et al 2023
STaSy Kim et al 2023
2023
CLLM Seedat al. 2024
TabEBM Margeloiu et al.
2025
TabDiff Shi ct 2025
Synthcity QQian 2024
2024
TVAE Xu et al. 2019
CoDi Lee er al 2023
TabSyn Zhang al.
SynMeter Du & Li
NRGBoost Bravo
Hansen et al 2023
Livieris et al. 2024
2025
TabStruct (Ours)
Kapar et al.
Paper
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B DESIGNS OF STRUCTURAL FIDELITY METRICS
In this section, we detail the design and computation of structural fidelity metrics. We first detail the computation Conditional Independence scores (Appendix B.I). and then detail the computation of the proposed global utility score (Appendix B.2
B.1 CONDITIONAL INDEPENDENCE (CI) SCORES
B.1.1 DERIVING CI STATEMENTS FROM A CAUSAL GRAPH
Goal. For each pair of distinct variables (æ,, objective is to construct: (1) family of d-separation sets S such that æ; 1 2g Sj,k, and (ii) a family of d-connection sets S3,x such that
J. L 3k Sj
Notations. We introduce the following notations, which will be used in the derivation of conditional independence (CI) statements:
Let 9 = E) denote a directed acyclic graph (DAG), where the node set x (W....,,DD. ID+1 consists of the variables introduced in Section
An undirected path P in G is sequence of distinct nodes (vi...., UL) such that for each edge on the path. (Ug, 1e+1)
or (ve-1, be) E E, and each 0y E X'.
A non-endpoint node on P is a collider iff the adjacent edges on P converge head-to-head at Ug (i.e. - 2/ < the induced subpath).
For disjoint subsets {æ,}, { S X, a path P is said to be blocked by S if either: (i) P includes a non-collider that is in S, (ii) P includes collider such that neither the collider nor any of its descendants is in S.
The variables xy and æ are d-separated by S3.6 (denoted æ, 1 æx (5,kk) if every path between zj and 24 is blocked by Sj.k-
Procedures. The derivations of CI statements are fully programmatic (Spohn) 1980 Dawid 1979 Constantinou Dawid 2017). For each pair variables
we enumerate all subsets S [.), 2t and apply the d-separation test (Tu et al. 2024 Spirtes et al. 2001) to the triple (m.,, Pk. S). If the test returns true, we add S the set Sj Once the d-separation sets are identified, we derive the corresponding d-connection sets by selectively removing elements from the Sj,6 sets. The full procedure is detailed in Algorithm
B.1.2 COMPUTE CI SCORES ON TABULAR DATA
We compute CI scores according to Equation (3). where the key step is select appropriate conditional independence test for different types of features. For categorical datasets (i.c., all variable are categorical),
employ the chi-square numerical datasets (i.e., all variables are numerical), we use partial correlation based on the Pearson correlation coefficient (Baba al. 2004). For mixed datasets (i.e., mixed variable types), we utilise residualisation based conditional independence test (Ankan & Textor [023) Li & Shepherd 2010) Muller & Peterson, 1984). We implement all conditional independence tests using pgmpy (Ankan & Textor 2024), an open-source Python library for causal and probabilistic inference. By default, the significance level set to 0.01 (i.c., the p-value 0.01).
of independence (McHugh) 2013). For
B.2 GLOBAL UTILITY SCORE
B.2.1 DOWNSTREAM PREDICTOR CONFIGURATIONS
To compute the utility per feature as defined in Equation (4) we need to evaluate the performance of downstream predictors when predicting the variable æj. which requires selecting an appropriate set predictors. As discussed Section the utility per feature is inherently affected by the inductive biases of downstream models. For instance. KNN tends perform better when the number of classes large (Jiang et al. 2024), whereas XGBoost often performs well on skewed target distributions (McElfresh et al.
2024). To mitigate such biases, employ ensemble of nine
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Algorithm 1 Derive complete CI statements
Input: DAG G over nodes X' (011..., LD+1}
Output: Full CI statements Cglobal
Cglobal f Ø
// initialise output
foreach unordered pair (j, ((a.b) ( |<a<b< do
Sj.k t Ø
// reset container
foreach S X (arj, 2x do if d--separation_eewt Leetnn_essssaa j. Bk, &x, then
S + S {S} Colobal + Colobal U ( 1 ax {)} // record conditional independence
// store separator
end end
foreach
S e Sj do
foreach v E S do
< S {u}
// candidate d-connection set
if not d- d-seppaaatoonneeette pettitiooo_tttt,,,,e_ Lk, then
Cglobal + Calobal U {(x) 1 æz {}} dependence
// record conditional
end end end end
return Cglobal
// complete CI statements
predictors with distinct inductive biases. Specifically, the widely adopted "AutoGluon- full" (Erickson et al.] 20200, which includes eight predictors, and supplement it with the competitive TabPFN (Hollmann al. 2025).
Furthermore, as shown in prior work (Kotelnikov et al. 2023), tuning downstream predictors can impact the relative rankings of tabular data generators, To account for this, we allocate time budget of one hour per feature for tuning the full ensemble. We refer to this configuration (i.c., using all nine tuned predictors) "Full-tuned"..
B.2.2 PRUNING THE ENSEMBLE OF DOWNSTREAM PREDICTORS
In addition to the "Full-tuned" setup, we define three alternative configurations of downstream predictors. These four configurations are summarised below:
Full-tuned: A tuned ensemble of nine predictors:
Logistic Regression (LR), KNN, MLP, Random
Forest, Extra Trees, LightGBM, CatBoost, XGBoost, TabPFN;
Light-tuned: tuned ensemble of eight predictors: Logistic Regression (LR), MLP, Random
Forest, Extra Trees, LightGBM, CatBoost, XGBoost, TabPFN;
Tiny-tuned: A tuned ensemble of three predictors: KNN, XGBoost, TabPFN;
Tiny-default: An untuned ensemble of three predictors: KNN, XGBoost, TabPEN.
An important observation is that tuning the downstream predictors does improve the absolute per- formance of the utility per feature. However, we find that global utility is more robust to the choice of downstream predictors than local utility. Specifically, when the ensemble reduced from nine to three predictors, the relative rankings of tabular generators under global utility remain consistent, whereas the rankings under local utility fluctuate notably. For instance, under local utility, CTGAN ranks second with "Fullltuned" but drops 10th with "Tfny-default".
We attribute this robustness to the faimess inherent in the design of global utility - each variable treated equally prediction target, thereby reducing the bias towards any specific decision boundary (i.e.. downstream predictor). This design helps to mitigate the effect of predictor-specific biases. Full experimental results are provided in Appendix E.4
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Practical guidance for computing local and global utility. For comprehensive and fair evaluation, TabStruct reports all results under the "Full-tuned" configuration. For local utility, we strongly recom- mend using the "Full-tuned" configuration. Using less robust setup may lead to unstable rankings and potentially misleading conclusions about generator performance. In contrast, Appendix [F.4 demonstrates that global utility remains consistent even under the "Tiny-default" configuration, as both "Full-tuned" and "Tiny-default" settings produce identical relative rankings across 13 tabular generators. Therefore, recommend using "Tiny-default" when computing global utility for model selection, particularly in scenarios where computational efficiency is a priority.
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C RATIONALES FOR EVALUATION FRAMEWORK DESIGN
C.I STRUCTURAL PRIOR FOR TABULAR DATA
The underlying structure of tabular data has long been open research question (Kitson et al. 2023
Hollmann et al. 2025 Müller et al. 2022: Haavelmo 1944, Wang & Sun 2022 Ucar ct al. 202 Zhu
al.] [023] Cui et al. 2024 Chen et al.) 2023b] Levin et al. 2023). For other modalities like textual data, it is natural to characterise their structure as autoregressive, guided by human knowledge (Yang) 2019). Therefore. pretraining paradigms aligned with the autoregressive structure, such as next-token prediction (Achiam et al., 2023), have proven successful in textual generative modelling. In contrast, heterogeneous tabular data does not naturally lend itself human interpretation, making a structural prior for such data generally elusive.
Recent studies (Hollmann et 2025 Müller al., 2022) on tabular foundation predictors have begun to shed light on the underly goggrryinggao structure of tabular data. TabPFN (Hollmann et al., (222) is tabular foundation predictor pretrained on 100 million "synthetic" tabular datasets. These datasets are "synthetic" because they do not incorporate real-world semantics: they are produced with randomly constructed structural causal models (SCM). Remarkably, despite not being explicitly trained on any real-world dataset, TabPFN is able to outperform an ensemble of strong baseline predictors, which have been fine-tuned on each individual classification task. The exceptional performance of TabPFN suggests that the SCMs used to construct the pretraining datasets, despite lacking real wolld semantics, effectively reflect the structural information encoded in real-world tabular data. However, it is important note that this does not imply SCMs can fully capture the underlying structure of all tabular data, as no definitive theoretical guarantees have been made yet in the tabular domain. Instead, TabPFN demonstrates that the causal relationships between features, as modelled by SCMs, serve as an empirically effective structural prior for a substantial proportion of real-world tabular data.
As the success of LLMs primarily stems from their ability leverage the autoregressive nature of textual data, we argue that a robust tabular data generation process should be able to capture the unique causal structures within the tabular data. More specifically, generating data aligned with the causal structures in reference data could provide valuable insights into the open research question of how to effectively leverage the structural information inherent in tabular data.
C.2 CPDAG-LEVEL EVALUATION OF STRUCTURAL FIDELITY
Prior studies (Tu et al. 2024 Spirtes et al. 2001 typically evaluate the causal structure alignment at three different levels: (i) skeleton level, (ii) Markov equivalence class level, and (iii) causal graph level.
Skeleton level is limited in capacity. At the skeleton level, all causal directions are ignored, resulting in a loss of information about the causal relationships between features. For instance, the causal skeleton is unable to reflect encoded physical laws. Consider the physical system illustrated in Figure [ the ground-trute truth causal path from p to FEarth is p + mA - FEarth This encodes a meaningful interpretation of physical law: given mA, changing P should force acting on ball A. However, if all directions are removed from the causal path, the resulting skeleton allows for alternative paths, such as p + ma < FEanhh which share the same undirected structure but imply contradictory physical laws. In this case, the alternative path suggests that, given MA. changing P would affect the gravitational force, which is incorrect. Therefore, we choose not to evaluate structural fidelity at the skeleton level due to its inability to capture reliable causal relationships across variables.
affect the gravitational
Causal graph level necessitates efficient and accurate causal discovery methods, which remains an open research question. At the causal graph level, structural fidelity assessed by comparing the directed acyclic graphs (DAGs) of the reference and synthetic datasets, accounting for both the skeleton and the causal directions of edges. In principle, this level provides the most fine-grained evaluation of structural fidelity. However, current causal discovery methods struggle to recover accurate DAGs from observational tabular data (Nastl & Hardt] 2024).. Section 4 and Appendix F demonstrate such limitations where Bayesian Network (BN) performs poorly generating high- quality synthetic data suggesting that existing causal discovery tools are inadequate for learning precise causal graphs.
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This limitation is well-documented in the literature: recovering perfect DAGs from tabular data remains an unresolved problem for current algorithms (Zanga et al. 2022 Kaddour et al. 2022 Nastl & Hardi 2024). This limitation further supports argument that CauTabBench provides limited insights for real-world datasets. While CauTabBench attempts to evaluate structural fidelity by applying causal discovery methods to infer "pseudo" causal graph from real-world data, the absence of ground-trute truth (GT) causal structures makes such evaluations unreliable. Without access known GT, it is impossible assess the validity of the inferred graphs. Moreover, the poor empirical performance of BN suggests that these pseudo causal graphs may not be accurate.
Moreover, evaluating at the DAG level requires running causal discovery algorithms on both the reference and synthetic datasets. Employing specific causal discovery algorithm may introduce evaluation bias analogous how utility scores are affected by the choice of predictor models. To reduce this bias, one would need to ensemble multiple causal discovery methods. However, unlike downstream predictors, causal discovery algorithms are often computationally expensive. For instance, the DAGMA algorithm (Bello et al. 2022) takes over 24 hours to recover causal graph from a dataset with more than 100 features on our machine (Intel(R) Xeon(R) CPU 2.20GHz, 64 cores), due to the exponential scaling of its computation cost with dimensionality.
CPDAG-level evaluation strikes a good balance between evaluation efficiency and validity. Unlike full DAG constructing via causal discovery. CPDAG-level evaluation does not require the orientation of all edges, making it a more tractable yet still meaningful metric of structural fidelity. A CPDAG represents the Markov equivalence class of DAG, preserving essential causal relationships while greatly reducing computational overhead. This is supported by the fact that Markov equivalent SCMs serve as minimal I-MAPs (Agrawal al. 2018) of the joint distribution factorisation p(X')
I p(z, pa (xz)). and no causal directions can be further removed. Therefore, the CPDAG-level evaluation provides a lens interpret the fidelity of the tabular data. As illustrated in Figure [ CPDAGs retain sufficient real-world semantics for practical use cases. Therefore, TabStruct evaluates structural fidelity at the CPDAG level, balancing semantic richness with computational feasibility.
It is important to note that even reference datasets do not guarantee CI scores of 1. This is analogous to ML efficacy, where even reference data cannot ensure perfect downstream utility (c.g.. balanced accuracy 1 or RMSE 0). However, shown in Section 4 and Appendix (F conditional indepen- dence (CI) tests generally provide valid and reliable evaluation results. Specifically, CI tests yield consistently high scores reference datasets, indicating their ability to distinguish between high- and low-quality datasets and thus produce meaningful fidelity assessments.
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D REPRODUCIBILITY
D.1 BENCHIMARK DATASETS
D.1.1 SCM DATASETS
To
accurately quantify structural fidelity, the reference data should be paired with ground-truth causal structures. To this end, we construct benchmark SCM datasets using structural causal models (SCMs) that have been validated by human experts (Scutari 2011). All 11 SCM datasets are publicly available, with further details provided in Table [ Table 6 and Table 7 By default, throughout this work,
references "six SCM datasets" refer to those listed in Table and Table
Table 5: Details of three SCM classification datasets from bnlearn (Scutari 2011
* Sumples
Features (2)
Numerical
Categorical
Classes
Samples
(Min)
Samples per class (Max)
Hailfinder
Meteorology
100,000
1785,71
56
25,048
44,200
Insurance
Bomomiies
100,000
27
3703.
27
1.648
$6,361
Sangiovese
Agricultuee
100,000
15
6666.67
14
16
5,659
6,841
Table 6: Details of three SCM regression datasets from bnlearn (Scutari 2011
# Samples
# Features
Dataset
Domain
N/D
Numerical
Categorical
(N)
(D)
Healthcare
Medicine
100,000
7
14285.71
4
3
MAGIC-IRRI
Life Science
100,000
1562.50
0
MEHRA
Meteorology
100,000
24
4166.67
20
4
Table 7: Details of five classification datasets with large SCMs from bnlearn (Scutari 2011
Dataset
Domain
Samples (V)
Features
(D)
N/D
Namerical
A Categorical
Classes
Samples per class
(Min)
# Samples per class (Max)
100,000
Diabetes
Science
100,000
242.
413
1,000
86,00)
Link
Life Science
100,000
721
138. 12
724
4
24,961
25.037
Pathlinder
Medicine
100.000
109
917 43
109
4
8,000
68,000
100,000
Human validation ensures that the causal structures realistic, thereby increasing the likelihood that TabStruct's s benchmark results can generalise to other real-world datasets where ground- -ruth SCMs not available. We note that this is core difference between TabStruct and prior studies (Tu et al.) 2024; Hollmann et al., 2025): rather than relying on toy SCM datasets lacking real-world semantics, TabStruct introduces of the first comprehensive benchmarks for tabular generative models, based on datasets with expert-validated causal structures, mixed feature types, and more than 10 features.
We outline the process of building the reference SCM datasets follows. Firstly, we ground-truth SCMs with realistic and expert-validated structures. Secondly, we perform prior sampling on these SCMs: root nodes randomly initialised, and their values are propagated through the causal graph. A single sample is generated by recording the node values after propagation, with each propagation producing one sample. Thirdly, this process is repeated until sufficient samples are obtained. In TabStruct, we set Nia = 100,000. By following this procedure, construct full datasets Dimll with accessible and well-defined causal structures. The pseudocode in Algorithm
D.1.2 REAL-WORLD DATASETS
To demonstrate the generalisability of the proposed global utility and TabStruct, we further select 23 challenging real-world datasets from the open- source TabZilla benchmark (McElfresh et al., 2024). the OpenML repository hattps://wwrr wwwp:/pw.ppp.l.mmmmmmmmmm. openml and the UCI repository (https: http///ariiieee ics. uci edu datasets).. All datasets are publicly available, with further details provided in Table and Table
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Algorithm 2 Constructing full SCM datasets
Input: Ground-truth structural causal model, M = (X, 9, F, E), number samples Nuil (default to 100,000 samples)
Output: Full SCM dataset Duu = (xx(1, ,y00) Mua
Pre-processing π +- TopologicalSort (9)
// topological order of the
variables
Dian < InitDataset ()
// Initialise an empty dataset
for i +- to Niut do
for j E do
if pa v (1)
Ø then Sample (E,)
// root node: random initialisation
else
- 1 (1 an E pa(æ;)), 62)
// Propagate through SCM
end
end
Append (Drun, (+11 dataset
// Add the new sample to the SCM
end
return Dulll
The dataset selection follows three main criteria: Firstly, the datasets are non-trivial, meaning that generative models cannot easily achieve evaluation results comparable to those obtained from the reference data. Secondly, the datasets originate from diverse domains. For example, "Credit-g" pertains business applications, whereas "Plants" relates biological studies. Thirdly, the datasets were not part of the meta-validation stage for TabPFN, reducing the likelihood that their causal structures were implicitly leaked during the development or pretraining of TabPFN.
Table 8: Details of 14 real-world classification datasets.
Datnect
Damii
Scamz
iD
Samples (N)
a Feaizecs
(EP
A/D
Numericl
4 Categnnial
Chonce
# Samples per ches (Mial
# Sumples per cles
(Ma)
Beanaiis
OpenML
3,400
Inzges
OpenML
Elecsiitt
OpenML
45.312
5034.67
19.237
OpenML
95,050
3351,03
lasmine
Lafe Sciencr
OpenMi.
41141
3,884
145
20.56
137
1,402
1,492
Numan
Baansmis
OpeMI.
45078
34,665
280.22
30
9,844
24,21
Phoneme
Language
OpenML
1489
5,004
900.67
1,586
3,515
Plans
Life Science
OpenMI
1491
1900
65
24,0
64
100
15
16
QSAR
Chenissy
OpenML
1494
1,05
42
25.12
356
699
SpeedDuing
Social Scieace
OpenML
40536
5.378
121
59:24
02
1,30
6,988
Spline
Iafe Science
OpenMi.
1
Traspororin
OpenM.
Inzges
OpenML
Table 9: Details of nine real-world regression datasets.
# Samples (N)
# Features
Dataset
Domain
Source
ID
(D)
N/D
Numerical
# Categorical
Ailerons
Physics
OpenML.
296
13,750
41
335.37
41
Califoria
Economics
OpenML
43939
20.640
2064.00
Elevvtoor
Physics
OpenML.
216
16,599
19
873.63
19
H16
Economics
OpenML.
574
22,784
17
1340.24
17
Liver
Medicine
OpenML
57.50
Sules
Economics
OpenML
42092
21,613
20
1080.65
18
Space
Demographics
OpenMI.
507
3,107
7
443.86
Superconductivity
Chemistry
UCI
21.263
82
259.30
82
Wine
Life Scienece
UCI
186
6.497
541.42
12
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D.2 DATA PROCESSING
Data splitting (Figure 5) For each dataset of N samples, we first split it into train and test sets (80% train and 20% test). We further split the train set into a training split (Drer) and a validation split (90% training and 10% validation). For classification datasets, stratification is preserved during data splitting. We repeat the splitting 10 times, summing up to runs per dataset. All benchmark generators are trained on Pief. and each generator produces synthetic dataset with NNof samples. For classification, the synthetic data preserves the stratification of the reference data.
Full Dataset
Niul
Training Validation data Nall x 0.8
Test
Ntest Niul X 0.2
Training split (Reference data) Nref N 0.8 x 0.9
Validation split
Naax 0.8 0.1
Evaluation dimensions
Generator
Synthetic data
Evaluation
Nayn = Nrrf
results
Figure 5: Data splitting strategies for benchmarking tabular data generators.
Feature preprocessing for generators. Following the procedures presented in prior work (McElfresh 2024 Grinsztajn et al. 2022), we perform preprocessing in three steps. Firstly, we impute the missing values with the mean value for numerical features and the mode value for categorical features. We then compute the required statistics with training data and then transform the training split. For categorical features, we convert them into one-hot encodings. An exception TabDifff which tends to perform better with ordinal encoding for categorical features. For numerical features, Z-score normalisation. We compute each feature's 's mean and standard deviation in the training data and then transform the training samples have mean of zero and variance of for each feature. Finally, we apply the same transformation to the validation and test data before conducting evaluations.
et al.
perform
Feature preprocessing for downstream predictors. The synthetic data produced by generators is inversely transformed back to the original feature space before being passed to the downstream predictors. In other words, the AutoGluon models receive input data in the original, unprocessed feature space, allowing them to apply their own model-speciff preprocessing strategies.
D.3 IMPLEMENTATIONS OF BENCHMARK GENERATORS
TabStruct includes 13 existing tabular data generation methods of nine different categories: (i) standard interpolation method SMOTE (Chawla et al. 2002): (ii) structure learning method Bayesian
Network (BN) (Qian al. 2024): (ii) two Variational Autoencoders (VAE) based methods TVAE (Xu et al.] 2019) and GOGGLE (Liu et al. (023):; (iv) Generative Adversarial Networks (GAN) method CTGAN [Xu et al. 2019; (v) normalising flow model Neural Spine Flows (NFL.OW) (Durkan et al.)
2019); (vi) free-based method Adversarial Random Forests (ARF) (Watson et al. 2023); y (vii) three
diffusion models: TP Kotelnikov et al. 2023), TabSyn (Zhang ct al. 2023). TabDiff (Shi et al.
2025): ; (viii) two energy- based models: TabEBM (Margeloiu al. 2024 and NRGBoost (Bravo
2025 and (ix) a Large Language Model (LLM) based method GReal (Borisov et al. 2023)
Following prior work (Kotelnikov al. 2023 Hansen et al.) 2023). tune the parametrised generators to ensure a fair comparison. Specifically. ly, we use Optuna (Akiba et al., (2019) to optimise each generator by minimising its average validation loss across 10 repeated runs. Each generator
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is given most two hours to complete single repeat. Importantly, to mitigate bias introduced by specific evaluation metrics, we tune each generator based on its own objective function rather than any external metric. Different from prior work (Du & Li 2024). this approach ensures that each model evaluated under conditions aligned with its intended optimisation direction. The technical details and hyperparameter search space for each method described below.
SMOTE an interpolation-base oversampling technique (Chawla et al., 2002), which generates syn- thetic samples by interpolating between existing minority class instances. We employ the open-source implementation of SMOTE provided by Imbalanced-leart (Lemaitre et al. 2017), where the number of nearest neighbours can be specified. Unless stated otherwise, we use the default setting
5. Bayesian Network (BN) is a probabilistic graphical model used to represent and reason about the dependence relationships between features (Qian al. 2024 Hansen et al., 2023). consists of two main components: (i) causal discovery model to construct a directed acyclic graph (DAG), where features and the target serve as nodes, and their dependencies are represented as edges; (ii) parameter estimation mechanism to quantify the dependence relationships. Following prior work (Hansen et al., 2023 the causal discovery method is selected from Hill Climbing Search (Koller) 2009), the Peter- Clark algorithm (Koller, 2009; Spiirte et al., 200TD, LiNGAM (Shimizu 2014), LiM (Zeng et al.) 2022), DAGMA (Bello et al., 2022). DCD Prashann et al. 2024). AutoCD (Chan et al. 2024), and Chow-Liu Tree-augmented Naive Bayes (Chow & Liu 1968 Friedman et al., 1997). We empirically find that AutoCD generally achieves the highest structural fidelity, and thus we build parametrised BN with AutoCD and maximum likelihood estimation.
Table 10: Hyperparameter search space of BN.
Hyperparameter
Range
struct learning score score
{'2",, "bdeu", "bic", "bds")
TVAE is a variational autoencoder (VAE) designed for tabular data (Xu et al. 2019). TVAE employs employs mode-specific normalisation to handle the complex distributions of numerical features. To address the class imbalance problem, TVAE conditions specific categorical features during generation.
Table 11: Hyperparameter search space of TVAE.
Hyperparameter
Range
encoder_n n_ m__layers_hhchee hidden
[1. 5
encoder_n hiideen
[50, 500
encoder_noome _noee_nnooiinn
{relu, Belu,,_eluure tanh, elu
LLunits_embeddee
500 500
decoder layers hidden
[1. 5
decoder n units hidden
|50 500
Recoder_nonlin
(relu, leaky_ relu_rrluu___ tanh. elu
n itterr Ir weight_decay
[100, 1000
10 10-31 (log)
[10 4, 10-3 (log)
GOGGLE is VAE-based tabular data generator designed to model the dependence relationships between features (Liu et al.) 2023). GOGGLE proposes learn an adjacency matrix to model the dependence relationships between features. However, TabStruct and prior benchmarks (Margeloiu (et al. 2024 Zhang et al., 2023 Shi et al. 2025) all show that the downstream utility of GOGGLE is limited. We hypothesise that this stems from the challenge of learning accurate structures of tabular data. The inherent structure learning mechanism in GOGGLE fails to capture accurate conditional independence relationships between features, which could thus lead to low- qualityl synthetic data. We further observe that the official implementation of GOGGLE (Qian et al., 2024) can be unstable and may fail to converge when fitted on large tabular datasets (e.g., more than 10,000 samples).
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Table 12: Hyperparameter search space of GOGGLE.
Hyperparameter
Range
encoder dim
322 128
encoder_1
1, 5
decoder dim
32, 128
decoder_arde arch
{gnn. het, sage
n _iter
[100, 500
learning rate
[10 5
10
(log)
weight decay
[10
10
3
(log)
alpha
[0.0, 1.0
beta
[0.0, 1.0
iter_opt
(True, False)
threshold
[0.0, 1.0]
CTGAN is conditional generative adversarial network (GAN) designed for tabular data (Xu et al. 2019). CTGAN leverages PacGAN (Lin et al.) (2018) framework to mitigate mode collapse. In addition, CTGAN employs the same mode-specific normalisation technique as TVAE.
Table 13: Hyperparameter search space of CTGAN.
Hyperparameter
Range
generator layers hidden
[1.
generator ___unts hidden conerator_nonlle
[50, 150
(relu, leaky_relu, relu, tanh,
discriminator_ ____________hh____ laydes_hiidenn hidden
11.
discriminator__ _i_________ Battiior_____u________ units_hidde
50, 150
discriminator_non nonlin
(relu, leaky relu, tanh, clu
iter
[100,
1000
discriminator iter
[1,
10 4 10 10
(log)
weight_decay
[10-1,
10
(log)
NFlow is normalisation flow model designed for tabular data generation (Durkan et al. 2019).
NFlow incorporates neural splines drop-in replacement for affine or additive transformations coupling and autoregressive layers, which assists in the modelling of tabular data.
Table 14: Hyperparameter search space of NFlow.
Hyperparameter
Range
n layerss hidden
layers_hidden
[1, 10
units hidden
[10, 100
tnneearttansform_tyy
(lu, permutation, svd] (affine-coupling.
base_transform__yye
quadratic-coupling
rq-coupling,
aifieresetoregeessivvee
rq-autoregressive/
dropout
0.00, 0.2
norm
False, True} 10 10-3 (log)
Ir
2 x 10
n iter
100, 5000]
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ARF is tree-based model for tabular data generation (Watson et al. 2023 ARF employs recursive
adaptation of unsupervised random forests for joint density estimation by iteratively refining synthetic data distributions using adversarial training principles.
Table 15: Hyperparameter search space of ARE.
Hyperparameter
Range
trees
{10. 20, .... 100
delta
(0, 2, 50}
max_ iiers
11
early_stop
(Tree, False
min node
{2, 4, 20
TabDDPM is a diffusion-based model for tabular data generation (Kotelnikov et al. 2023). TabDDPM introduces two core diffusion processes: (i) Gaussian noise for numerical features and (ii) multinomial diffusion with categorical noise for categorical features. TabDDPM directly concatenates numerical and categorical features as the input and output of the denoising function. We further note that the official implementation of TabDDPM (research 2023) can be unstable and may fail to converge when fitted on tabular data with mixed feature types.
Table 16: Hyperparameter search space TabDDPM
Hyperparameter
Range
n n_iter Ir
[10 10a)
[10-3 5 10 (log)
bright_decar
[10 4,
10 10-3 (log)
num_timest num_timesteps
[10, 10
TabSyn is diffusion-basee model for tabular data generation (Zhang al. 2023 It synthesises tabular data by employing a diffusion model within the latent space of a variational autoencoder (VAE). TabSyn supports wide range of data types by mapping them into unified representation space and explicitly modelling inter-column dependencies.
Table 17: Hyperparameter search space of TabSyn.
Hyperparameter
Range
vac.num epochs
[100,
1000]
vae.max beta
[10 3
10
2 (log)
vae.min beta
[10-5 10
(log)
vae.lambd
0.1 1.0
vae.num layers
1,
vae.d token
1.
vac.n head
1,
fac.factor
1, 64
vac.Ir
[10 4 10
(log)
vae. wd
0, 10 (log)
tabsyn.num_eponn secucs
[100, 500]
tabsyn.Ir
[10 1, 2 (log)
wd
0, 10 (log)
TabDiff is a diffusion- based model for tabular data generation (Shi et al. 2025). introduces a joint diffusion framework capable of capturing the mixed-type distributions inherent in tabular data within a single model. In particular, TabDiff utilises a joint continuous time diffusion process and leverages transformer architecture to handle both numerical and categorical variables.
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Table 18: Hyperparameter search space TabDiff.
Hyperparameter
Range
batch size
[112, 1024, 2048, 4096, 8192)
l_lambda
[0.1, 10.0
check_val val_everry
{10, 20, 30, 40, 50)
floss_weight
schedule -cheuut
("constant" "anneal" "linear"
lambda
[0.1, 10.0
ema_decay
0.9, 0.9999
factor
[0.1, 0.99
110 10-2) (log)
Ir scheduler
("reduce_ la____r________________ cotooonn_paa'
"cosine", "none"
reduce_ Ir patience steps
{10, 30, 50, 70
{100, 200, 300, 500)
weight_decay
[0, 10 10 (log)
TabEBM is energy-based model for tabular data generation (Margeloiu al. 2024). It transforms a pretrained tabular predictor into a set of class-specific generators. While the original paper only provides TabEBM implementation for classification tasks, extend its applicability in TabStruct to regression tasks by treating all reference samples as single class, and then performing sampling over the energy surface.
Table 19: Hyperparameter search space of TabEBM.
Hyperparameter
Range
starting_ Locitt_oo_tt___eeeeeeeeie pwwnt_noiie__aeeeeeeeepeeenooee std
[10 10
(log)
sgid step_size size
[10 10
(log)
sgld noise_ std
[10- 10
(log)
steps
{50, 100, 200, 500}
NRGBoost is an energy-based model for tabular data generation (Bravo 2025) It is trained by maximising local second-order approximation to the log- likelihood each stage of the boosting process. NRGBoost is shown to offer generally good discriminative performance and competitive sampling performance compared to more specialised alternatives.
Table 20: Hyperparameter search space of NRGBoost.
Hyperparameter
Range
num trees
[1, 10, 20, 50)
shrinkage
[0.01, 0.3
max_leaves
{32, 64, 128, 256, 512)
max_ratio in_ num mmodll_smmple {10,000, 40,000, 80,000, 160,000)
[1,
p_ refresh
00.01, 0.3
num chains
{4, 8, 16, 32)
burn in
{50, 100, 200, 500)
GReaT leverages large language models (LLMs) to generate synthetic tabular data (Borisov et al. 2023). GReaT converts each sample into sentence and fine-tunes the language model to capture the sentence-level distributions. Additionally, GReaT shuffles the order of features to mitigate the permutation variance in sentence-level distributions.
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Table 21: Hyperparameter search space of GReaT.
Hyperparameter
Range
n iter
{100, 300, 500, ]
learning rate
[10-4 10 (log)
weight decay
[10-5 10 (log)
D.4 HYPERPARAMETER TUNING FOR DOWNSTREAM PREDICTORS
As discussed in Appendix B.2 employ AutoGluon's 's built-in tuning functionality for training the ensemble predictors. For each variable, the ensemble predictor is allocated one hour of tuning budget per repeat, resulting in total of 10 hours per variable for each dataset. We note that TabPEN is not integrated into the employed version of AutoGluon. However, the default configuration of TabPFN already demonstrates competitive performance (Hollmann al. 2025). and thus, we its default hyperparameters across all of our experiments.
D.5 AGGREGATION OF EVALUATION RESULTS
The reported results are averaged by default over 10 repeats. We aggregate results across all SCM or real-world datasets because the findings are consistent across classification and regression tasks.
Specifically, we use the average distance to the minimum (ADTM) metric (Grinsztajn et al., [022]
McElfresh et al. 2024 Hollmann et al. 2025 Margeloiu et al. 2024: Jiang et al. 2024) via affine renormalisation between the top- top- pop-performing and worse-performing models.
D.6 SOFTWARE AND COMPUTING RESOURCES
Software implementation. (i) For generators: We implemented SMOTE with Imbalanced- learn (Lemaître et al., 2017). an open-source Python library for imbalanced datasets with an MIT license. For TabSyn and TabEBM, we used their open-source implementations with an Apache-2.0 license. For TabDiff and NRGBoost, we used their open-source implementations with an MIT license. For other benchmark generators, we used their open-source implementations in Synthcity (Qian) al. 2024), library for generating and evaluating synthetic tabular data with an Apache-2.0 license. (ii) For downstream predictors: We implemented TabPFN with its open-source implementation battps://qittne
com/ aut h We implemented the other eight downstream pre- dictors (i.e., Logistic Regression, KNN, MLP, Random Forest, Extra Trees, LightGBM, CatBoost, and XGBoost) with their open-source implementation in scikit-learn (Pedregosa et al.) 201 and Au- toGluon (Erickson et al. (020)), an open-source Python library under an Apache-2.0 license. (iii) For data preprocessing and evaluation: All data handling, including data loading and preprocessing, was performed with TabCamel (Jiang 2025a), an open-source Python library for tabular data management. All data-quality evaluation was performed with TabEval (Jiang 20256) and Synthcity (Qian et al. 2024), comprehensive open-source Python framework for evaluating tabular data. (iv) For resulf analysis and visualisation: All numerical plots and graphics have been generated using Matplotlib 3.7 (Hunter 2007). Python-based plotting library with a BSD license. The icons for evaluation dimensions in Figure 2 are from ht tps: /tt::////coo.... http//iiconccoo///oo
We ensure the consistency and reproducibility of experimental results by implementing uniform pipeline using PyTorch Lightning, an open-source library under an Apache-2.0 license. We further fixed the random seeds for data loading and evaluation throughout the training and evaluation process. This ensured that all benchmark models in TabStruct were trained and evaluated on the same set of samples. The experimental environment settings, including library dependencies, specified in the open-source library for reference and reproduction purposes.
Computing Resources. All the experiments were conducted machine equipped with an NVIDIA A100 GPU with 80GB memory and an Intel(R) Xeon(R) CPU (at 2.20GHz2) with 64 cores. The operating system used Ubuntu 20.04.5 LTS.
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E EXTENDED ANALYSIS AND DISCUSSION
E. EXTENDED ANALYSIS ON VALIDITY OF BENCHMARK FRAMEWORK
The benchmark datasets present a genuine challenge for existing generators. As detailed in Section 4 select challenging, contamination-free real-world datasets, ensuring that they non-trivial for existing tabular data generators. Table illustrates that, unlike prior studies (Shi) al. 2025 Zhang et al., 2023 Margeloiu et al. 2024), no generator can easily match Dier our benchmark datasets. This confirms that the selected datasets offer a more informative and realistic assessment of generator capabilities.
Detection score (C2ST) relatively limited in measuring global structural fidelity. Following prior work Zhang et al. (202)), we compute the detection score (C2ST) using logistic regression classifier. Higher C2ST scores indicate better performance, i.e., synthetic data that is harder to distinguish from real data. We select three SCM classification datasets (Table[3:: Hailfinder, Insurance, and Sangiovese. Table 22 shows that C2ST exhibits weaker correlation with global CI compared to global utility. The relatively low correlation between C2ST and global CI is consistent with the trends observed in other sample-level metrics, including a-precision and f3-recall Although these sample-level metrics are designed to capture high-order interactions across features, they fail to explicitly attend to inter-fcature causal interactions, limiting their ability to reflect the underlying causal structures. This further supports the effectiveness of global utility in assessing global structural fidelity of tabular data.
Table 22: Spearman's rank correlation with global CI on three SCM datasets. We bold the highest correlation with Global CI. Global utility correlates strongly with global CI (p < 0.001). demonstrating the validity of global utility.
Global CI f
a-precision
0.38
8-recall
0.47
C2ST
0.50
Global utility (Ours)
0.83
E.2 EXTENDED ANALYSIS ON VALIDITY OF GLOBAL UTILITY
The evaluation results are consistent across classification and regression datasets of different domains. In Table 23 SMOTE remains one of the most competitive methods for capturing local structure, and diffusion models consistently rank among the top-3 for modelling global data structure. These findings indicate that the proposed "utility per variable" metric is stable and provides a unified lens for interpreting evaluation results across both classification and regression datasets.
we present per-dataset evaluation results for both local and global utility.
Global utility provides similar generator rankings as global CL Figure 6 demonstrates that the rankings of generators under global utility closely align with those under global CI. Notably, the Top-3 methods are identical across both metrics: TabSyn, TabDDPM, and TabDiff. In contrast, when using local utility, the Top-3 methods shift SMOTE, CTGAN, and TabDiff. This reveals a great discrepancy between the rankings produced by global CI and those from the local utility. In comparison, the proposed global utility yields rankings consistent with global CI, indicating that global utility is an effective metric when ground-truth SCM is unavailable. Consequently, global utility serves as an informative metric for evaluating global structural fidelity.
In addition to the correlation analysis of metric values, we compute Spearman's 's rank correlation between the generator rankings induced by three metrics: local utility, global CI, and global utility. As shown in Table 24 across 13 generators evaluated on six SCM datasets, generator rankings induced by global CI and global utility exhibit a strong correlation (r, = 0.95, < 0.001), whereas local utility shows substantially weaker alignment with the other two metrics.
We further analyse the rank correlations among the top-5 generators according to global Cl: Tab- DDPM, TabSyn, TabDiff, TVAE, and ARF. When restricting the analysis to the top-5 generators
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Table 23: Top-3 tabular generators across the TabStruct benchmark suite. For each dataset, we report the Top-3 tabular generators in terms of both local and global utility. For visualisation, we abbreviate "Classification" "Class.", and "Regression" as "Reg." ". The results indicate that while SMOTE remains simple yet effective approach for ML efficacy, diffusion models demonstrate stronger capability capturing the holistic structure of tabular data.
Dataset
# Samples (N)
Features (D)
N/D
1st
Local utility 2nd
3rd
1st
utility 2nd
3rd
SCM datasets
Claxk
Haillinder
100,000
56
1785.71
SMOTE
CTGAN
NRGBoot
TabDDPM
TabSyn
TaDDiT
Insurance
100,000
27
3703.70
SMOTE
TaBEBM
TVAE
TasDDPM
TabDir
TabSyn
Sangiousse
100,000
15
6066.67
SMOTE
CTGAN
TabEBM
TabDDPM
TabSyn
TVÁE
Healthcare
100,000
14285.71 71
SMOTE
TabDiT
TahSyn
BN
ARF
TaDDDPM
MAGIC-IRRT
100,000
64
1562.50
SMOTE
TVAE
TahSyn
TVAE
TaPDDPM
TahSyn
100,000
TahSyn
GOGGLE
TabDDPM
TahSyn
Real-world datasets
Ada
4,562
48
95.04
SMOTE
TabEBM
TabDiT
TVAE
TabDDPM
ARF
Characters
10.218
1277.25
SMOTE
TabEBM
ARF
TabDDPM
TabSyn
TabDiT
Credit-g
1,000
21
47.62
SMOTE
TabEBM
TabDiff
TahSyn
TabDiff
TabDDPM
Electricity
45,312
5034.67
SMOTE
TabEBM
TahDii
TabDDPM
TahDiff
ARF
Higgs
SMOTE
CTGAN
TabDDPM
TabSyn
Jasmine
2,984
145
20.58
SMOTE
TVAE
TahSyn
TabSyn
TabDiff
TahDIPM
Clavs.
Nomao
34,465
119
289.62
SMOTE
CTGAN
TVAE
TabDir
TYXE
TANDDPM
Phoneme
5,404
900.67
SMOTE
TabEBM
NRGBoost
TaaDDPM
TabSyn
TaDDIT
Plants
1,599
65
24.60
SMOTE
TabEBM
NRGBoost
Ta6DDPM
TaSSen
TabDif
QSAR
1,055
SMOTE
TabEBM
NRGBoost
TabSyn
TahDIPM
TaNDiff
SpeedDating
8,378
121
69.24
SMOTE
TabEBM
TVAE
TabDDPM
TasSen
TANDiT
Splice
3,190
SMOTE
TabSyn
TabDai
Vehicle
846
19
44.53
SMOTE
TabEBM
TabSyn
TabSyn
TaPDDPM
TabDiT
Zemike
2,000
48
SMOTE
TabEBM
TVAE
TabSyn
150DDPM
TabDiff
Allerons
13,750
41
335. 37
SMOTE
TabDiff
TahSyn
TabDiff
TahDDPM
TabSyn
California
20.640
2064.00
SMOTE
TahSyn
TahDiff
TabDDPM
TakSyn
TaNDiT
Elevatoes
16,599
19
873.63
SMOTE
TabDil
TahSyn
TabDDPM
TabDiT
TabSyn
H16
22.784
17
1340.24
SMOTE
TabDift
CTGAN
BN
TabDDPM
TaDDif
Liver
345
57,50
TabDiff
TahSyn
SMOTE
ARF
TabDiff
TabSyn
Sales
21,613
20
1080.65
SMOTE
TabDiff
TahSyn
TahDiff
TabSyn
TVAE
Spuce
3.107
TahSyn
TahDin'
TabSyn
Superconductivity
21.263
82
259.30
SMOTE
TabDif
TaSSyn
BN
TaNDiI
TabSyn
Wine
6.497
541.42
SMOTE
TahSyn
TahDil
TabDif
TabSyn
TabDDPM
based on global CI, Table shows the correlation between global CI and global utility remains high (r, = 0.92, < 0.001). This suggests that global utility maintains a consistent ranking even among high-performing generators, supporting its robustness discerning top-performing models.
Generalor runking under different metrics
SMOTE
2
BN
TVAE
GOGGLE
4
CTGAN
5
NFoow
ARF
7
TaPDDPM
TabSyn
TahDiff
TaFBBM
10
NRGBoost
GReal
12
Local utility
Global CI
Global utility
Figure 6: Rank comparison of 13 tabular data generators across three evaluation metries on six SCM datasets. Compared to local utility, global CI and global utility rankings relatively consistent, suggesting that global utility can serve as an effective metric for global structural fidelity.
Global utility consistently aligns with global CI on large-scale SCMs. To further validate the applicability of global utility in high-dimensional settings, we select five additional datasets (Table
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Table 24: Spearman's rank correlation based on generator rankings on six SCM datasets. Global utility induces generator rankings correlating strongly with global CI, showing the alignment between global utility and global CI (p < 0.001).
Local utility
Global CI
Global utility
Local utility Global CI Global utility
0.29
0.35
0.95
Table 25: Spearman's rank correlation based on generator rankings of the top-5 generators (by global CT) on six SCM datasets. Global utility maintains consistent ranking even among high-performing generators, showing robustness in discerning top-performing models (p < 0.001).
Local utility
Global CI
Global utility
Local utility
Global CI
0.38
Global utility
0.32
0.92
with large-scale SCMs from the bnl onre repository (Lemaître et al. (017). Table 26 demonstrates that global utility remains strongly correlated with global CI across both these large SCM datasets and the six smaller ones discussed in Section 4 The results provide further empirical evidence that global utility reliably captures the global structural fidelity of tabular data.
Table 26: Spearman's rank correlation with global CI on SCM datasets. We bold the highest correlation with Global CI. Global utility correlates strongly with global CI across 11 SCM datasets (p < 0.001), demonstrating the generalisability of global utility.
Dataset
Shape
Tread
o-prccision
A-recall
DCR
A-presasce
Local unilit
Local CI
Global utility (Ours)
5. datasets with large SCMs
0.26
0.34
0.31
0.33
-0.25
-0.22
0.13
0.11
0.51
11 SCM datasets Section large)
0.40
0.30
0.36
0.46
40.30
-0.26
0.13
0.19
0,83
Normalised utility is important for providing balanced and consistent evaluation across columns. To further assess the impact of normalisation, we compare global utility computed using absolute predictive scores versus relative (i.e., normalised) scores. As shown in [7] using unnormalised scores leads substantially weaker correlation with global CL. Specifically, Spearman's 's drops from 0.84 to 0.57. This finding supports that the normalisation design plays an important role in improving alignment with causal structures. Furthermore, global utility based on absolute scores fails to produce stable generator rankings across different predictor configurations. Specifically, the Top-5 generators under Full-tuned and Light-tuned settings share only one generator common when computing global utility with absolute scores. This further supports that the normalisation enables global utility to deliver more robust and consistent evaluations across predictor configurations.
Metrics requiring explicit causal discovery remain limited in evaluating the structural fidelity of tabular data. We further examine the relationship between global CI and several metrics used in CauTabBeenhh, which rely causal discovery algorithms infer SCMs from observed data. Specifically, we construct two dataset collections, A and B, each comprising three SCM datasets: (=Hailiind, Insurance, MEHRA] } and B=(Saggiovese, Healthcare, MAGIC-IRRI). For datasets in A. we compute our global utility metric alongside three Cau TauBenncchh metrics: skeleton-F1, direction-ACC. and direction-F1. For datasets in B, we compute the global CI. We then calculate Spearman's 's rank correlation between global CI and each of the other metrics. Table 28 shows that global utility exhibits substantially stronger correlation with global CI than the metrics from CauTh. The relatively weaker correlation of CauTabBench metrics is likely due to their dependence on causal discovery algorithms. For instance, skeleton-Fi Fl uses PC algorithm to recover causal graphs from synthetic tabular data. However, PC algorithms could suffer notable performance degradation as the number of features increases (Zanga et al. 2022 Zeng et al.] (202)). This observation aligns with broader findings regarding the limitations of existing causal discovery
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Table 27: Spearman's rank correlation with global CI on SCM datasets. We bold the highest correlation with Global CI. Global utility with normalised utility correlates strongly with global CI, showing that normalisation helps global utility provide balanced evaluation across columns.
Global CI f
Global utility (absolute performance) Global utility (relative performance)
0.57
0.84
methods on real-world tabular datasets (Nastl Hardt 2024). These results suggest that global utility offers more robust, SCM-free approach for evaluating global structural fidelity of tabular data.
Table 28:
Spearman's rank correlation with global CI across six SCM datasets. We bold the highest correlation with Global CI. Global utility exhibits a substantially stronger correlation with global CI compared to the CauTabBench metrics < 0.001), which rely on causal discovery.
Global CI f
skeleton-F1
0.42
direction-ACC
0.44
direction-FI Global utility (Ours)
0.44
0.84
Metrics for evaluating multi-table interactions are insufficient for structural fidelity within a single table. Prior work (Pang et al. 2024 Solatorio & Dupriez 2023). such ClavaDDPM (Pang et al. 2024), which models relational databases, proposes the use of machine learning efficacy (MLE) assess how well generator preserves inter-table relationships. These studies primarily focus on relational structures across multiple tables, whereas TabStruct is designed to evaluate inter- feature causal relationships within a single table. Consequently, the prior studies do explicitly establish a direct connection between MLE and the underlying causal structures of a single table. To quantitatively assess such a distinction, we evaluate the correlation between MLE and global CI using the same experimental setup for global utility. We strictly follow the MLE evaluation procedure proposed in ClavaDDPM, following its official implementation (Pang et al., 2024). As shown in Table 29] both MLE-R2 and MLE-FI exhibit relatively weak correlations with global CI, suggesting that multi-table relational metrics are less suitable for evaluating inter-feature causal interactions in single-table scenarios.
Table 29: Spearman's rank correlation with global CI across six SCM datasets. We bold the highest correlation with global CI. Global utility generally shows a stronger correlation with global Cl compared to the metrics designed for multi-table settings (p 0.001).
Global CI f
MLE-R2
0.40
MLE-FI
0.44
Global utility (Ours)
0.84
Global utility provides stable results with synthetic data of equal size to reference data. Across six SCM datasets 3 and T)ble/ we fix Nia while varying the ratio Nief NNmm We evaluate three representative tabular generators: SMOTE, TabSyn, and TabDDPM, which achieve the best results in local CI. global CI, and global utility, respectively. Table 30 shows that When Nayn < Naya- global utility generally increases with the sample size of D Dsya. Once the condition Dayn > D Dayn is met, global utility tends to stabilise. This observation further validates the robustness of global utility score and supports our design rationale for using equal-sized Dayn and D in the evaluation framework.
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Table 30: Global utility scores under different synthetic sample sizes. We bold the highest global utility score for each generator. In general, global utility tends to saturate when the synthetic sample size reaches or exceeds that of the reference data.
Noe: : Nsya
SMOTE
TabSyn
TabDDPM
5:1
0.13
0.62
0.64
3:1
0.25
0.72
0.74
1:1
0.39
0.76
0.80
1:3
0.39
0.75
0.79
1:5
0.38
0.76
0.81
E.3 EXTENDED ANALYSIS ON STRUCTURAL FIDELITY OF GENERATORS
Column order can have a notable impact on autoregressive tabular generators. Autoregressive generators model the data distribution by linearising features according to a column order л. For tabular data, the ideal ordering x¹ corresponds to the topological order derived from the true SCM. However, since x typically unavailable in practice, using mismatched æ may compromise structural fidelity. Although prior work (Borisov et al. 2023) attempts to improve robustness by finetuning LLMs on randomly permuted column orders, such approaches are computationally expensive (e.g., we observe that GReaT often fail to converge datasets with more than 50 features) and do not explicitly align the model with the true causal structure of the dataset. For instance, if the random ordering π happens reverse the topological order encoded by the ground-truth causal structure, the autoregressive model is forced to learn spurious conditional independence across features, thereby harming the learned global structure. To investigate the impact of directional bias, we conduct proof-of-concep experiment on six SCM datasets. Specifically, we introduce "GReaT-sort", a variant of GReaT finetuned using the ground-truth topological order extracted from each SCM. In this setup, GReaTT-sor and the original GRea'T share identical model configurations, and the only difference lies the column order employed during finetuning. As shown in Table GReaT-sort consistently outperforms GReaT across all datasets by clear margin, suggesting that the mismatched bias in column ordering constrains the performance of autoregressive tabular generators.
Table 31: Global utility of GReaT and GReaT-sort on six SCM datasets. We bold the highest performance for each dataset. GReaT-sort consistently achieves higher global utility than GReaT, indicating that aligning column order with the underlying causal structure can effectively improve the performance of autoregressive tabular models.
Generator
Hailfinder
Insurance
Sangiovese
Healthcare
MAGIC-IRRI
MEHRA
GReaT
0.29 10.28
0.32 0.49+0.14
0.3 0.31 10.8
0.19 0.1910024 10:24
0.41
0.24 1024
0.26
GReaT-sorted
0.43
0.40++023
0.43
0.49
0.31
Interpolation and energy-based methods tend to prioritise local structure over global structure. Figure (3 (right) shows that the interpolation method (e.g.. SMOTE) and energy-based models (e.g., TabEBM and NRGBoost) can effectively capture local structure, yet perform poorly when modelling global structure. These two families of methods share a common trait in their generation process: they generate new samples from class-specific reference data. For example, in classification tasks, SMOTE interpolates between samples of the same class, and TabEBM samples from a class-specific energy surface. As a result, the generated samples are inevitably biased towards local structure.
A high global utility score typically reflects consistently high utility across individual features. As shown in Figure 7 generators with relatively high global utility scores (Type 1), such as TabSyn and TabDiff, tend to achieve balanced utility across features. This is largely because the global utility assigns equal importance to each feature, thereby reducing bias towards any particular one. As result, generators with high global utility are less prone to overfitting a limited subset of features, thus achieving balanced performance across features. In contrast, generators with lower global utility scores generally fall into two categories (Type 2 and Type 3). The models of Type 2, including SMOTE and CTGAN, often achieve high utility on the target feature (i.e., local utility) but perform poorly the others. This pattern primarily stems from their target-specific model design, which
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inherently biases them towards the target feature. This is consistent with Figure (Right), which shows that such models prioritise capturing the local structure of the target feature at the expense of the global structure. The models of Type typically underperform across all features. We attribute to their misaligned architectures for the unique characteristics of tabular data. A representative example is GRea'T, which attempts to leverage domain knowledge from L.MMs for tabular data generation. However, the mismatch between the textual modality of LLMs and the heterogeneous nature of tabular data undermines their ability model tabular structures effectively.
"Hailfinder" dataset (Classification)
"Insurance" dataset (Classification)
"MEHRA" dataset
(Regression)
usiityys 0:54
SACOPe
19ndea Syed beat baa
Type High global utility with relatively balanced utility across features
IChabe sitthye Levat 4t
Tokdon
12hbbl Leret aetteeet
1535
iGsba utlitter Local Lt 2tilter.000
cbal GG.ttel 101
1shbbl sit fore Local unlltess.
ind
Tectare mides
CreAM
ClOAS
Type global utility, but highly performant in local utility
Tetur Edc
Fora ido
Texure inse
Type Low global utility with generally poor utility across features
Figure 7: Utility score distribution across features. For visual clarity, we present seven representa- tive generators and report their utility scores for each feature, accompanied by standard deviations. The results reveal that generators generally fall into three distinct categories: Generators with high global utility scores tend to exhibit balanced performance across all features. In contrast, those with relatively low global utility scores either display strong local utility or show generally poor performance across features.
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E.4 EXTENDED ANALYSIS ON PRACTICABILITY OF GLOBAL UTILITY
Global utility remains stable across different downstream predictors. Figure g shows that the relative rankings of tabular generators consistent even when the number of downstream predictors is reduced from nine to three. In contrast, local utility is far more sensitive to the choice of predictors: its rankings fluctuate greatly even when simply reducing from nine eight predictors. The instability of local utility stems from its bias towards the prediction target, which may introduce unfair bias towards specific types of predictors. For example, KNN tends to perform better when the number of classes is large (Jiagg et al.) 2024), while XGBoost typically favours skewed target distributions (McElfresh et al. 2024). Since local utility evaluates performance on a single feature, such biases are amplified, yielding unstable rankings even after ensembling different predictors. In contrast, global utilityy aggregates performance across all features, diluting predictor-speciffe biases and producing more robust generator rankings.
Global utility is stable regardless of hy hyperaaraeeter tuning. Figure shows that global utility provides consistent rankings of tabular generators regardless of whether downstream predictors tuned. We note that this does not imply that tuning unnecessary. line with prior work (Kotelnikoy et al. 2023 McElfresh et al.) 2024 Du & Li 20244,, also observe that tuning improves absolute performance. However, tuning has negligible effect on the relative rankings under global utility. In contrast, local utility necessitates tuning guarantee reliable results. Such robustness further reflects the core rationale of global utility: by not focusing on single feature, it avoids introducing feature-specific biases and is therefore less susceptible variation caused by tuning for particular downstream prediction target. Such robustness further supports the rationale for using global utility as stable and unbiased evaluation metric.
Cencroraan (palicm
SMOTE
BN
TVAE
GOGGLE
10
CTGAN
NFlow
13
Full-tuned
Light-tuned
Tiny-tuned
Tiny-default
ARF
Genmrsee üifeeilleet proktee.
TabDDPM
TabSyn
TabDiff
TabEBM
10
NRGBoost
GReaT
Full-tuned
Light-tuned
Tiny-tuned
Tiny-default
Figure 8: Comparison of ranking stability between global utility and local utility on 23 real- world datasets, evaluated using different downstream predictors. The proposed global utility produces consistent generator rankings across downstream predictors. In contrast, local utility necessitates a large set of tuned downstream predictors (i.c., Full- aull-tuned) to yield meaningful rankings. As result, global utility achieve high computational efficiency with only small ensemble of default predictors (i.e., Tiny-default in Figure 4
Global utility has the potential evaluate global structural fidelity in the presence of latent confounders. We present proof-of-concep: experiment to investigate the behaviour of global utility on datasets containing unobserved confounders, using three SCM datasets: Sangiovese, Healthcare, and MEHRA. Given SCM, introduce neceaf exogenous latent confounders U {UI..... U Uncee where each Us ~ (0, 1) is associated with a child set Sş C such that [S&] = m2 E (2,3, 3, 4). For each variable z, Sg. modify its structural function via x = (pa(z))), + EkyEs. AuGUK. where the U₁ exogenous and mutually independent, and ÄR; Unif(0.5, 1.5) controls the strength of confounding. This process yields causal graph denoted @Conf We then marginalise out the
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unobserved confounders to convert F into maximal ancestral graph (MAG), IMAG. from which we derive conditional independence (CI) relationships using m-separation (Sadeghi & Lauritzen 2014). Based on Equation (3), compute "Global CI (MAG)", variant of standard global CI. using the derived CI relations on the MAG. Global utility maintains stable performance (Table and strong correlation with Global CI (MAG) (Table 33) across different numbers of unobserved confounders, These results highlight the robustness and generalisability of global utility, and they suggest its potential for evaluating global structural fidelity in datasets containing latent confounding.
Table 32: Benchmark results on three SCM datasets with injected unobserved confounders, aggregated over 13 tabular generators. Global utility provides stable performance evaluations across varying numbers of unobserved confounders, demonstrating its robustness in assessing tabular data structures with latent confounding.
Local CI (MAG)
Local utility
Global (MAG)
Global utility (Ours)
1
0.03
0..02
0.80
0.79
2
0.84
0.84
0.80
0.77=0.02
3
0.81
0,85+0.02
0.75
0.79=0.04
4
0.80=0.03
0.84
0.74
0.75=0.03
5
0.79
0.82
0.71 10.04
0.77=10.22
Table 33: Spearman's rank correlation with global CI (MAG) three SCM datasets with injected unobserved confounders. We bold the highest correlation with global CI (MAG). Global utility consistently exhibits a stronger and statistically significant correlation with global CI (MAG) compared to other metrics (p < 0.001).
Shape
Trend
a-precision
3-recall
DCR
6-presence
Local CI (MAG)
Local utility
Global utility (Ours)
1
0.26
0.30
0.41
0.24
-0.28
-0.23
0,22
0.14
0.76
2
0.30
0.41
-0.17
-0.16
0.14
3
0.22
0.31
0.40
0.27
-0.25
-0.16
0,18
0.19
0.76
0.22
0.31
0.39
0.25
-0.26
-0.15
0.15
0.19
0.75
0.33
0.26
-0.28
-0.16
0.16
0.72
Global utility is indicative of data utility for downstream causal inference tasks. We perform causal inference evaluation across 13 tabular data generators on six SCM datasets. Following the protocols ohen et al. (202aa) and Cau'l TabBechh (Tu et [2024), we assess performance by learning SCMs from synthetic data and comparing them against ground-truth SCMs on both interventional and counterfactual inference tasks. For interventional evaluation, we apply 10 interventions per variable and generate 100,000 interventional samples per intervention under both Mer and Mayn- We then compute the interventional mean squared error (I-MSE) by comparing the expected values of the remaining variables. For counterfactual evaluation, given observed data, we apply 10 interventions per variable and generate 100,000 counterfactual samples using both Mar and Msyn- We compute the mean counterfactual values from both SCMs and calculate the counterfactual mean squared error (C-MSE). As shown in Table 34 the top five performing generators in the causal inference evaluation (TabSyn, TabDDPM, TabDiff, TVAE, and ARF) are consistent with those ranking highest in both global CI and global utility. This further supports the utility of global utility as indicator of global causal structure in tabular data. Table also also shows that existing evaluation metrics exhibit considerably weaker correlations with causal inference performance, whereas global utility remains reliable and effective indicator.
Global utility provides stable evaluation across different degrees of data availability. We select six SCM datasets (Table[5)and Table and simulate varying levels of data availability by subsampling to smaller values of Nual- The corresponding reference sample size N = Nuwll X 0.8 x 0.9, as illustrated in Figure 5 As shown in Table 36. the proposed global utility metric consistently achieves the highest correlation with global CI across all evaluated sample sizes, clearly outperforming existing evaluation metrics. Notably, this holds even in very low-data scenarios. such Nuai & 500. These results suggest that global utility serves as a robust and reliable measure for global structural fidelity across a wide range of data availability.
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Table 34: Causal inference check of synthetic data from 13 tabular generators six SCM datasets. We bold the lowest error for both interventional and counterfactual tasks. Diffusion models generally achieve the best perfomance in downstream causal inference tasks.
Generator
I-MSE
C-MSE
SMOTE
0.32
0.45
BN
0.37
0.51
TVAE
0.16
0.27
GOGGLE
0.59
0.75
CTGAN
0.87
0,90+0.04
NFlow
0.97-0003
0.98
ARF
0.12=0.02
0.23
TabDDPM
0.10
0.22
TabSyn
0.09
0.20 10002
TabDiff
0.09
0.2 +0.02
TabEBM
0.34
0,47+0000
NRGBoost
0.55
0.70
GReaT
0.59
0.75+0.00
Table 35: Spearman's rank correlation between causal inference metries and other metrics on six SCM datasets. We bold the strongest correlation with causal inference performance. Global utility exhibits a strong correlation with causal inference metries (p 0.001), showing that global has the potential to indicate causal inference evaluations in SCM-free settings.
Shape
Trend
o-precision
3-recall
DCR
6-presencc
Local utility
Local CI
Global CI
Global utility (Ours)
IMSEL 0.32
0.33
-0.35
0.19
0.23
0.15
0.21
.0.17
-080
-0.90
C-MSE
-0.17
-0.40
-0.16
-0.14
0.36
0,21
-0.45
-0,24
-0.82
-0.83
Table 36: Spearman's 's rank correlation with global CI across different degrees of data availahility. We bold the strongest correlation with global CI for each degree. Global utility consistently correlates strongly with global CI, showing it a stable measure for global structural fidelity given different degrees data availability (p 0.001).
Nan
Shape
Trend
a-precision 3-recall
DCR
ò-presence
Local utility
Local
Global utility (Ours)
100
0.40
0.51
0.36
0.46
.0.41
.0.37
0.20
0.26
0.82
0.43
0.51
0.32
0.52
-0.49
-0.39
0.24
0.22
0.83
1,000
0.43
0.46
0.35
0.53
-0.49
-0.42
0.22
0.19
0.87
5,000
0.47
0.41
0.42
0.50
-0.48
-0.45
0.18
0.13
0.83
10,000
0.46
0.55
-0.47
0.14
100,000
0.47
0.47
0.37
0.49
-0.43
-0.40
0.14
0.22
0.84
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TabStruct provide customised results on global structural fidelity evaluation. We consider two variants of global Cl: (i) Global CI (discrete), which is the current global CI reported in Section 4 and (ii) Global CI (continuous). Instead of using binary CI test outcomes as in Equation (
compute the average a level at which CI tests fail across all features to obtain a continuous global
CI score. Similarly, we consider variants of global utility: Global utility (continuous), which is the current global utility reported in Section 4 and (ii) Global utility (discrete). Instead of normalised downstream performance in Equation 4 we perform Wilcoxon signed-rank test (a 0.01) between Perr(D and Perf(D) for each feature, then average the resulting binary outcomes. Table 37 shows that all variants of global CI and global utility, both continuous and discrete, exhibit strong mutual correlations. Notably, their correlation strengths are very similar, ranging between (0.80, 0.86), indicating consistent alignment across formulations, which allows users to select either the continuous or discrete variant for global CI and global utility.
Table 37: Spearman's 's rank correlation based on generator rankings on six SCM datasets. The variants of global CI and global utility stably shows strong correlation, indicating that global utility is an effective and robust measure for global structural fidelity (p < 0.001).
Global CI (discrete)
Global CI (continuous)
Global utility (continuous) Global utility (discrete)
0.84
0.86
0,80
0.83
E.5 PRACTICAL GUIDANCE
Evaluation dimensions are complementary, not interchangeable. Table Table[]shows shows that no single metric is fully indicative of all other metrics. Therefore, researchers and practitioners should select evaluation dimensions that align with the specific objectives of their tasks, rather than relying on a single dimension. If the objective is leakage- free data sharing. the privacy preservation and ML efficacy should be prioritised over density estimation and structural fidelity. Conversely, when the aim is to model a real-world physical system like Figure | global structural fidelity should take precedence, because it promotes realistic inter-feature relationships, instead of being distorted towards a single prediction target.
SMOTE is a simple yet effective method for ML efficacy. In Table 23 we provide per-dataset guid- ance for selecting appropriate tabular generators based on ML efficacy. Surprisingly. SMOTE achieves the highest local utility on 28 out of 29 datasets, Despite this strong performance, Table 4 shows that it has been largely overlooked in prior studies (Shi et al. 2025 Bravo 2025 Xu et al. 2019). We strongly encourage researchers and practitioners to consider SMOTE as a robust baseline in scenarios where MI efficacy is the primary objective and other dimensions, such as privacy, are less critical. For instance, in data augmentation tasks, SMOTE can serve as an effective baseline to compare against.
E.6 FUTURE WORK
Investigation using separate independent set for performance evaluation. Different from the well-established experimental setup in Section 4 we can modify the data splitting strategy into Durin DieM= : Dindep Dealtd = 3: 3 3 1. In this configuration, Dindep acts as independent benchmark to assess whether a generator is underfitting or overfitting the training data. Figure 9 shows the proof-of-concept results on three SCM datasets (Table An interesting observation that SMOTE outperforms D Dindop in the Trend metric but performs much worse in DCR. This indicates that SMOTE generally overfits the training data Duain- rather than learning truly generalisable distributions. In addition, FigureDisuggess Suggesss that simply maximising DCR can degrade performance in other aspects, such as density estimation. Therefore, although some generators demonstrate high DCR scores, they may not be ideal if they severely compromise on other metrics. Therefore, achieving a higher DCR than Dindep may be a more balanced and practical criterion for acceptable privacy preservation, rather than pushing DCR to its maximum. We further observe that varying the data splitting strategy can have notable impacts on model performance. For instance, TabDiff excels in Trend under the original splitting strategy (Section 4 but underperforms in the new configuration. We attribute this to model-specific propertics. As the new strategy allocates fewer samples for training. it implies potential limitation for fitting tabular generators. Specifically, TabDiff appears more
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susceptible to reduced training sample sizes than other benchmark methods. As TabStruct is fully open-source and will continue to evolve with contributions from the community, we believe that incorporating an independent set holds promise for offering fresh and valuable perspective in assessing the performance of tabular data generators.
Data (han)
1.00
Feet Data (hano
1.00
7400
10.56
Rext (ndees)
16.53
SMOTE
10.77
CTOAN
0.55
505yt
10.5ym 10.02
10.00
0.70
CTGAN
0.57
10.24
164
0.53
TV4
SMOTE 9..03
Rea Data (hail 6.08
0.00
0.40
0.00
100
0.02
0.20
0.40
0.50
50
1.00
0.00
9:20
0.40
0.00
1.50
150
Shope
Tord
DC1 Scoe
Figure 9: Benchmark results of six representative tabular generators three SCM classification datasets with separate independent set. The results show that Dindep, i.e., orange bar, offers novel and complementary perspective for evaluating the performance of tabular data generators.
Theoretical justifications for causal modelling of tabular data. Bridging the gap between empirical metrics on real-world tabular datasets and structural causal models (SCMs) remains a
major theoretical challenge in causal machine learning (Nastl & Hardt 2024 Tu al. 2024 Zanga
et al. 2022). A promising direction for future research lies in developing theoretical underpinnings for the proposed global utility metric. Currently, the proposed global utility serves as an empirically effective metric for structural fidelity, grounded in its correlation with conditional independence (CI) scores. more rigorous formalisation could help enhance interpretability in relation to specific causal relationships, and potentially inspire new paradigms for evaluating tabular generators.
Efficient and accurate causal discovery real-world scenarios. promising direction for future work is the development of more effective causal discovery algorithms for real-world tabular data. In practical scenarios, ground-truth causal graphs are seldom available, and despite progress constraint- based, score-based, and hybrid approaches, reliably recovering even partial or probabilistic SCMs remains a challenge particularly in high-dimensional settings (Zeng et al.) 2022 Kaddour et al. 2022 Nastl & Hardi, 2024). Nevertheless, incorporating such approximated structures as priors or regularisers in the global utility computation could enhance both its scalability and its fidelity to causal semantics. This would not only enable structural fidelity evaluation
complex datasets but also improve the robustness of global utility by reducing the influence of spurious statistical associations.
Structure-aware tabular data generation. Beyond evaluation, another important avenue for future work is the design of structure-awar tabular data generators that are explicitly optimised for structural fidelity. These models could embed inductive biases or incorporate regularisation objectives that encourage alignment with the conditional independence structure observed in the reference data. This would mark shift away from conventional likelihood-driven generation toward structure-informed tabular data generation, enabling the generation of data that better complies with domain-specific constraints (e.g., scientific laws in Figure T..
Extension to dynamic and temporal data modalities. While TabStruct already offers broad coverage of static tabular datasets (Appendix (A), a promising direction for future work to extend the framework to support temporal and event-based data, where causal relationships may change over time. Many real-world domains - such as healthcare, finance, and operations research - exhibit longitudinal structures that challenge the assumptions of static SCMs (Borisov et al. (022). Adapting global utility to reflect deeendepn causal structures would broaden TabStruct's 's applicability.
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F EXTENDED EXPERIMENTAL RESULTS
F.1 EVALUATION RESULTS FOR SCM DATASETS
F.1.1 CLASSIFICATION DATASETS
Table 38: Raw benchmark results of 13 tabular generators on "Hailfinder" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CI". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utility or local CT), while diffusion models typically excel at capturing global structure (i.e., global CI global utility).
Generator
Trend
Demeity Eatimation o-precision
fl-rccall f
Privacy Preservation DCR
4-Presence
MI. Efficaey Local unility
Local CI
Structural Fiddlit Global CI
Global unlity
Dat
L.00_.00
1,00
1,00
1.00,000
4.00
g.00
1000
ga
L000
SMOTE
0.99
0.98 iome
0.89
1.90
g.00
1.00
1.95
0.89 ja:s
0.53
0.40
BN
0.99-119
0.98
2.99
0.3 0.39
0.642m00
0.00aum
0.662124
0.19
0.52-211
0.36,200
TVAE
0.94_110
0.50
0.86gaa7
0.1 0.8
2.66
0.01
0.92gnm
0.78
0.61-a11
0.66.2013
GOGGLE
0:94_430
0.86
0.37
0.43
0.19 1p4i
0.62
0.53
0,51
0.29
0.93
go90
0,96
jose
1.0e
0.73 j2:1
4533
NFlow
2.8
0.74ggno
0.00g000
8.68.00
0.02
0.52
0.53
0.53
2.04
ARF
0.96.491 54
0.93
0.91 an0x
0 0.28
0.54
0.66
081 1mm
0.57 2315
0.55_
0:54g
TaNDDPM
0.90
0.85
0,5
0,23
200e
0.01 1000
0.54
0.18
0.66
0.72
TahSyn
0.81 0.81.036
0.64,aze
0.73
0.22
0.22
1.96
0.81
0.74.317
0.71
0,71
TahDii
0/M5gaas
0.62.a
0.68
TakEBM
..94_.43
0.90
a.88
0.34
0.39
0.34
0.77.a915
0.51
0.30
NRGBoust
0.93 0.9
0.89 core
0.86
0.22
a.5
0.02
0.93
0.73 0.73
0:47 aa:9
GReaT
0.94.112
0.89
0.86
0.37 20ee
0.43
0.19
0.62
0,53
0.51
0.29 0,29
Table 39; Raw benchmark results of 13 tabular generators on "Insurance" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CI". SMOTE generally achieves the highest performance capturing local structure (i.e., local utility or local CD), while diffusion models typically excel at capturing global structure (i.e,, global CI or global utility).
Generator
Shape
Trend 1 o-precisiinn 1
Density Extimation
ffrecall 1
Privacy Presersation DCR
A.Presence
MI. Rflicacy Local utility"
Local CI
Structural Fidelity Global CI
Global unility
Dat
L.0
1.00
L000
1.00
0.00
g.00
1.00
1.00
0,97
L.00
SMOTE
0,99 -0
0.99
0.97
0,93
g.00
100
0.86
0.53
g.43
0.99--19
0,95
0.65
0.48
0.00
0.66-2.11
0.55-318
0.31
TVAE
8.97_490
0.70
2.5
0.00
anm
0.67 29
0.58
GOGGLE
0.95 0.95_.41
0.92
0.90
1010
1.02
0.82 1015
0.57
0.52
0.32
CTGAN
0.91
0.91
0.92 jo04
0.69 jom
0.01 200e
0.99
0.76
0.49
0.33 0,33
NElow
0.92.892
2.86
0.79
0 0.23
0.562006
0.02
0.73
0.50
0.51
2.21
ARF
D497.434
0.54gam
0.64
0.91
0,86
0.81 2014
0.59
g.00
g.81
0.51
0.64.
0.72
TahSyn
0.87.411
0.76
0.72
0.36
0.16
0.22
0.92
0.82:211
0.66.
0.67
TANDKI'
8.98_44
0.96amm
0.96gnns
0.6400
0.2920m
0.00
0:99
0.72
0.60)_214
0.67.20-3
TaFBBM
D.98..41
0.96
1.95
042,000
0.1611177
000
1,02.001
0.80)_311
0.51_a54
0.34g
NRGBoust
0.94.433
0.85
0.37
0.23
0.02
1 1.00
0.79
0.49
0.19 4232
GReiT
0.95.a31
0.9
0,90
3.20
0,02
0.2
0.57
0.52.aa15
0.32.g227
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Table 40: Raw benchmark results of 13 tabular generators on "Sangiovese" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CI". SMOTE generally achieves the highest performance capturing local structure (i.e., local utility or local CI), while diffusion models typically excel at capturing global structure (i.e., global CI or global utility).
Generntor
Shape
Dendity Estimation preciision
f-recall f
Privacy Preservation DCR
5.Presence
ML Effecacy usility
Structural Fidelity
uniliyy
D&r
L.00.030 30
1.00
1.00ga00
1.00a0e
0.00
0.00
1.00auuc
0.99
0.99
L.00aa00
SMOTE
0.99 1.99
1.9%
0.90
0.88
a.23
0.00
0.96
0.79
0.56
0.41
RN
0,99
2.97
0.95
0 30
0.37
000gue
0.52
0.53
0:53
0.20
TVAE
0.95
0.36yoni
0.1
0.62.a11
0.76
0.96..31
1.95
0.93
0.44
1.05
0.60
0.56.2ae
0.55
0.95
2.95
0.31
suu
0.91
0.73
0.50
0.90a2225
NElow
0.89 0.89
0.89
0.82
0.15
0.32
0.4
0.41
0.54
0.51
0.20
ARF
0.97.831
0.95
0.93
0.44
a.29
0.04
0.76,00
0.62.104
0.59
0.60
ToNDDPM
0.98-132
0.97suc
1.45
0.18
0.00mmm
0.63
0.77-am1
0.84
TahSyn
0.97-331
2000
0.73-a.1
0.81
0.97-.91
0.94
0.93
0.34
0.28
2.69
0.65
0.66
TabEBM
0.97
0.97
0.95
0.36
0.38
0.00
0.91
0.80
0.56:a1s
0.30
NRGBoost
0.98-1122
0.91swe
0.89
0.29
0.30an04
0.46
0.59
0.76.2.1
0.53
0.17:021
GReaT
0.96__91
g.95
0.93
0.44
4.28
0.05
0.00
0,56
0.55
0.31
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F.1.2 REGRESSION DATASETS
Table 41: Raw benchmark results of 13 tabular generators "Healtheare" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "Cr". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utility or local CI), while diffusion models typically excel at capturing global structure (i.e., global CI or global utility).
Generator
Shape
Trend 1 o-precision 1
Deadity Estimation
A-recall ?
Privacy Preservation 5-Presence
DCR
ML Effecayy Local utility ?
Local CI
Structural Fidelity Global CI
Global unility
Pat
1,00.030
5.00
g,00
1 1.00000
5.00
0.00
1.00aac
0.96
0.98
1.00
SMOTE
0.89
2.0
2,00
1.09
2.00
0.00
101 10m
0.74.231
0.60.a.11
0.50
-. 50
go9%
0,98gn
0.02000
g00e
0.0gmmm
0.72
0.65
2.900
TYAE
0.89 34
0.93
0.96
0. 0.14
g.00
0.71 2017
0.55
0.58 1::1
0.57 a.57 20:3
GOGGLE
0.71 20:
0.77
0.59
0.18 0.18
0.01 0.01 a00e
24.60
0.72
0.67
0.52
0,17 0.17
CTIAAN
0.83-022
0.90zac
0.89
0
0.00aaze
0.31 2n42
0.724
0.67
0.52-a32
0.15
NElow
0.87_443
1.88
1.02.am
0.36
0.48
0.50.aa1
0.14g
ARF
1000
1,00).00m
0.47 jool
4.00
1000
0.49..22
0.64.
TahDDPM
1.92
0.96.am
0.38
0.00aaze
0.4
0:41 2022
0.53
0.72.s239
0.82
TahSyn
0.81-:34
01865au1
(.81
0.19
0.06:1ue
1.34
0.84
0.6992212
0.71
0.78
TahDiff
0:88..33
0.83
0.96
1002
1.04
0.86
0.67
0.69
0.81
TabEBM
0.85-025
0.85aam
0.95
0.18
0.12
0.58.308
0.58.a2s
0.44
NRCiRoost
0.80
0,92
18
0.07
0.19
0.68-2213
0.52-3a2
0.16
GReaT
1.85
0.89gum
0.89
0.05
0.09
0.34
0.51
0.52.ga1e
0.19
Table 42: Raw benchmark results of 13 tabular generators on "MAGIC-IRRI' dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "Cl". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utility or local CI), while diffusion models typically excel at capturing global structure (i.c., global CI or global utility).
Demsity Estimation o-precision 1
Privacy Preservation DCR
ML Eliiaay utiliyy
Structural Fidelity Globul CI
Generator
Shape
A-recall 1
6-Presence
Local CL
Global unllity
Per
1.00gmm
1,00ga9)
1.00gm0
0.00gare
0.00gmm
1.00gmi
0.99
0.99
1.00g000
SMOTE
0.96.119
1.00
0.36
0.98
0.40
0.00amm
0.98.10
a.57
0.54
0.41
BN
0.94_as>
2.99
2.19
0.51gom
2.39
0.54
0.56gm0
0.52_aro
0.59
0.66.
TYAE
0.91 0,91_430
0.99
0.51
0.70
1.53
0.00
0.96
0.53 La04
0.58_a.0
0.86
DOGGLE
0.73-925
0.99
g.31
0.55
0.562114
6.462122
0.95uum
0.51
0.45-a19
0.33
CTCAN
0.73
0.52
0.42
200
0.54_aa04
0:47:a16
0:43
NFlow
0.90 31
0.27 Lnoz
2.04
0.83 10.r
0.09_am
0.46.a14
g.33
ARF
0,99 .039
1.9
0.83
0.20
0.44
1.00
0.58
0.51
0,57
0,76
TaNDDPM
0:47.032
1.00
0.81
a.5
0.26
0.00.ue
0.6
0.51
0.63.a2e
a.83
TahSyn
D.96-444
1.000me
0.75ga14
0.54.010
0.44.mm
0.0
0.63_ar4
0.83
0.97__432
1.00
0,80,
0.44
0.00
0.97
0.55 jaz0
0.64.a25
0.82
TahEBM
0.96.431
4.9
0.79
0.22033
0,30
0.0 aovo
0.8 10:4
0.52
0.54
0.37
NRCiRoost
0.99
0.77
0 36202
0.01 som
0.91
0.55
0.48
0. 0.34gpar
GReaT
0.94_431
0.99
0.66,005
0.55
0.42.000
0.55
0255p0
0,50
0.49
0.41 2031
Table 43: Raw benchmark results of 13 tabular generators "MEHRA" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CI". SMOTE generally achieves the highest performance capturing local structure (i.e., local utility or local CD), while diffusion models typically excel capturing global structure (i.e., global CI or global utility).
Demsity Estimation
Privacy Preservation DCR
ML Ellicay Local udiity
Structural Fidelity Globul CI
Generntor
Shupe
Trand 1 o-precision 1
A-reall
A-Presence
Local CI
Global utility
Per
1,00_a
1.00
1 1.00
0.00
0.00
1.00g0e
0.96
0.96.at1
1.00
SMOTE
0.97 0.97_499
0.94
2.89
2.03
0.00
0.94
0.55 2915
0.54_a15
0.42.
0.39
g.0
13
0.66gmm
0.49
0.55
0.55 gm:n
TYAE
0.89
2.87
0.95
0.43
a.07
0.22
0.85
0.55
0.51
0.62
GOGGLE
0,70-922
0.80
0.66
0
0.30
0.10
12,80220e
0.562nm
0,5f.a214
0,51
0.30 0.30
CTGAN
0.83
0.86gmm
0.97 gm07
0.43
2.05
0.07 2016
0.56ge05
0,54_am4
0,50
0.28
NFlow
0.85_441
0.84
0.90
4.37
0.10
0.63 snow
0.51
0.18 Ja18
0,50_ara
0.21
ARF
0,91
0.9
0,97
0.38
0.06210
0.004000
0.68
0.18-a19
0,51
TiNDDPM
0.88
0.47
2.05
000
0.6
0.47
0.57=at5
0.73
TabSyn
0.84_4434 04
0.80
0.89
0.44
3.07
0.56
0.58
0.57.ar4
0.68
TahDiff
0.86
1.88
0.95
0.39
1.08
1.06
0.54
0.55
0.57..ss
0.73
TahEBM
0.85_19
0.87amm
0.96gom
0 0.24cc
0.
0.0
0.6420
0.49.904
0,53
0.32
NRCIBoost
0.92__43
0885g11
0/6
0.51
4:27.4-15
GReaT
0.83 088
g.86
0.77gam
j,38
g008
0.17
0.55
0.50
0.26
51

---

Published as a conference paper at ICLR 2026
F.2 EVALUATION RESULTS FOR REAL-WORKS DATASETS
F.2.1 CLASSIFICATION DATASETS
Table 44: Raw benchmark results of 13 tabular generators on "Ada" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CT". SMOTE generally achieves the highest performance capturing local structure (i.e., local utility or local CI), while diffusion models typically excel at capturing global structure (i.e., global CI or global utility).
Density Estimation eeprrciison
Privacy Preservation DCR &-Presence
MI Efficacy Local utility
Structural Fidelity Glohal utility
Generator
Shape
Trend
8-recall
DRst
1,00gam0
1.00.0m
1.00
1,00.000
g.00
0.00
1,00
1.00
SMOTE
0.24
0.89 0.89
0.76
0.04
0.00
1.01
0.47
BN
203r
0097
0.83
2.25
0.16
0.86
0.36
TVAE
0.23
0.98.amm
0. 0.70
0.22:s0::
0.28
0.05
0.96=0m
0.77=013
GOGGLE
0.36gam
0.97.am
0.78 20.12
:.3
g.24
0.26
0.88 0.11
0.36
CTGAN
p.22
0.97
1.90
0.15
0.22
0.03
0.95
0,29 0,291.mm
NElow
0.23gmue
0.97
0.87 2007
0.07=002
g.20
0.02
0.87-012
0.53
ARF
0.24
0.98.20
0.96
0.24
0.26
0.00=a000
0,94_0.9
0.73
TabDDPM
0.35
0,93
0.50
0.21 :0.1
0.10:000
0.22
0,88-.012
0.74.0.
TabSyn
g.29
0.91
g.54
0.19
p.22
0.32
0.98-amr
0.73
TabDiff
0.44
0.96
0.80
0.19
0.33
0,21
0.98-min
0,70
0.43
0,982am
0.93
0.27=0.13
0.24
0.01
0.98-aun
0.36
NRGBoost
0.30
0.96.aom
0.45
0.19:000
0.29
2.07
0.98-am
0,20
GReaT
0.36
0.97.om
0.78
0.31
0.21
0.26
0.88
0.36
Table 45: Raw benchmark results of 13 tabular generators on "Characters" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, abbreviate "conditional independence" as "CI". SMOTE generally achieves the highest performance capturing local structure (i.c., local utility or local CI), while diffusion models typically excel at capturing global structure (i.e., global CI or global utility).
Density Estimation
Privacy Preservation DCR
ML Efficccy utility
Structural Fidelity Global utility
Generator
Shape
Trend f a preccision
8-recall f
6-Presence
Doc
1.00gam
1.00
1.00
1,00go0:
0.00ga00
0.00
1.00gam
1.00gam
SMOTE
2.83
0.9
0.99
0.41 0.41
0.06
0.00
0.97=005
0,40
BN
0.85 2om
pmm
0,98
0.01
0.32
0.01 0.01 3:000
0,30
0.08
T TVAE
0.91 .p0
0.95
0.04
g.31
0.01ga00
0.77
g.4
GOGGLE
0.93
0. 2096
0.19
g.23
0.01 =000
0.40-a03
2.19
CTGAN
0.802am
0.93-aom
0.94
0.02-z0m0
0.30
0.02
0.75
=.07
NElow
in82
0.88 0.88:gom:
0.94
0.00.amm
0.41
0.02
0,20-aam
0.02
ARF
g.8
0.89
1.99
0.11gam
g
g.00
0.82_mm
2.49
TabDDPM
0.95 0.84
0.98
0.17
0.16
0.01
0.46_
0.76
TahSyn
a.84
0.92.am2
0.95
0.14-00m
0.20
=0,0
0.79_022
0.69
TabDiff
0.86
0.90
0.96
0.12.s0.2
0.23
0.01
0.80-02:
0.66
TabEBM
0.95
0.98 1000
0.16
0.31
1,00
0.88_015
g.25
NRGBoost
0.te
0.92.mm
0.97 +0.00
0.12
0.28
0.01
0.77_034
0,11 g.11
GReaT
a.79
0.89
0.89 0.89
0. 12.22.012
0.31
0.04
0.29-001
0.10
52

---

Published as a conference paper at ICLR 2026
Table 46: Raw benchmark results of 13 tabular generators on "Credit-g" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CT". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utilitty or local CT), while diffusion models typically excel at capturing global structure (i.e., global CI or global utility).
Density Estimation
Privacy Preservation DCR 6-Presence
MI. Efficacy Local utility
Structural Fidelity Global unility 1
Shape
Trend 1 c-precision
8-recall f
Der
gm00
1000
1.00
2000
g.00
0.00
1.00_am
1,00
SMOTE
2.95
0.90.om
0.871000
0.79 2.m
g.00
1.17_030
0.42
BN
0.97
0.95 2.9
0.97
0.68
0.06
0.00
0.92-mmm
0.39
TVAE
0.86
0.80
0.48-0oz
g.04
0.02=001
1.11=034
0.47=014
GOGGLE
0.79
0.67
0.55
0.35
0.36
0.37
1,05=0336
0.33
CTGAN
n.80
0.72.00m
g.83
0.27=007
g.50
0.21 2:016
1.13
0.21
NElow
0,90ga.1
0.84_aomt
0.84
0,27
0.50
0.02=0001
0.85
0.24
ARF
0.97
0.86
0.98
0.45::02
0.53
0.00
0.87 0,87
0.43
TabDDPM
1.23
0.45
0.28
g.17
15
0,91-am
1.55
TabSyn
0.86
0.76.2013
0.67
0.41
0.44
0.03
1.15g031
0.64
TahDiff
g.90
0.74g014
0.91
0.40-0.17
D.43
0.02
1.15-031
0.62+a.19
TabEBM
0.92
0.84_om
0.93
0.50
0.38
0.02
1.15
0.33
NRGBoost
0.75
0.34
g.38
2:00
1.15_051
g.25
GReaT
gm88
0.80
0.64
0.43
0.42
0.10ga0e
0,91_mm
0,26
Table 47: Raw benchmark results of 13 tabular generators on "Electricity" dataset. We report the normalised mean +'t std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CT". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utility or local CI), while diffusion models typically excel at capturing global structure (i.e., global CI or global utility).
Density Estimation
Privacy Preservation DCR
ML Efficacy Local utility
Structural Fidelity Glohal uillity 1
Shape
Trend 1 o- precision
8-recall f
6-Presence
D
1.00gam
1.00.am
1.00
..00..mm
0.00
0.00
1.00
1.00
SMOTE
0.86
0.99
0.99
0.78
0.01 20,00
0.00
0.98-a022
2.41
BN
0,93
0.97
0.97
0,98
0.21
0.05 Loos
0.01 0.01
0.75
0.23 0.23
0.0
0.92.am
0.96
0.20=a0:
a.09
0.21
0.90-aox
0.56
GOGGLE
0.86
0.91 .om
0.93
0.33
0.07
0.43
0.76
0.27
CTGAN
n.86
0.92gmm
0.96
0.19 0.19 201
g.02
0.01 go0
0.92_am
0.21 gasi
NElow
0.84
0.85
0.91 0.91
0.09
0. 0.14gm06.
0.03
0.75
0.25
ARF
0.862am
0.81 20.4
0.95
0.26=
0.02
0.00
0.90=aot
0.62
TabDDPM
0.87
0.95-amm
0.98
0.32
0.03
0.77
0.76
TabSyn
0.54
0.73
0.48
0.20
0.12
4.77
0.60
TahDiff
0.88
0.96
0.23
0.06gnbs
0.03
0,93_min
0.75
TahFBM
0.90
0.92-aam
0.97
0.21 0.21
0.21
0.03
0.93
0.26
NRGBoost
0.87
0.92:am:
0.97 0.97+800 +000
0.22::015
0.04:ao1
0.03
0.92-am
0.22
GReaT
0.86
0.91
0.93
0.33
1.07
0,43
0.76_n12
0,27
53

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Published as a conference paper at ICLR 2026
Table 48; Raw benchmark results of 13 tabular generators on "Higgs" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CT". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utilitty or local CT), while diffusion models typically excel at capturing global structure (i.e., global CI or global utility).
Density Estimation
Privacy Preservation
MI. Efficacy Local utility
Structural Fidelity Global unility 1
Shape
Trend 1 c-precision
8-recall f
DCR 6-Presence
Der
1.00
1.00
1.00
g.00
g.00
1.00_am
1,00
SMOTE
g.90
0.99 10m
0.76
0.82
a.12
g.00
0.99
g.45
BN
0.99 m.92
0.98
0.29 0.29
0.06
0.00
0,85
0.24
TVAE
n.86
0,97
0.92
003
0.25
0.12
0,93
0.63
GOGGLE
0.90
0.97=20.
0. 0.90
=.40
0.13 2.13
0.12
0.84_000
0.29
CTGAN
0.97.00
0.95
0.32.g0zz
0.09 0.09 s/00
0,95_u115
0.23
NFlow
0.83
0.95.a0m
0.87
0.23
0. 0.18g006
0.69
0.77=0.4
0. 26.60.000
ARF
0.88
0.95
0.91 1:000
0. 0.26
0. 1.030
0.00
0.89
0.50 0.50
TabDDPM
0.92
0.97
1.93
0.42.00s
0.06
g.10
0.80
TabSyn
0.91 ante
0.97
0.94
0.38
0.14
0.10
0.95
0.76.024
TahDiff
0.96
0.85
0.27=022
0.20
0.1 0.11
0,95
0.70
TabEBM
0.91
0.97
0.93
0.25
0.26
0.10:0.99
0.95
0,22
NRGBoost
0,91
p.97
0.78 0.78 10:13
0.25
0.11
0.12
0,95_am
0.18
GReaT
g.90
0,97
0.90
0.40
0.13gate
0.12ga09
0.84_mm
0,29
Table 49: Raw benchmark results of 13 tabular generators on "Jasmine" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CI". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utility or local CI), while diffusion models typically excel capturing global structure (i.e., global CI or global utility).
Density Estimation o- precision
Privacy Preservation DCR
ML Efficacy Local utility
Structural F Fidelity Glohal millity 1
Shape
Trend 1
8-recall f
6-Presence
D
1.00gam
1.00.am
1.00
1.00..om
0.00
0.00
1.00
1.00
SMOTE
0.98
0.98
0. 0.86
0.82
0.06gn01
0.00
0,98-a.2
0.46
BN
0.96
0.94_nos
0.84
0.36
g.39
0.13
0.91 aam
0.42.aas
0.96
0.94
0.8 0.83
0.28
2.49
0.14
0.97=012
0.47=a010
GOGGLE
0.95
0.91
0091
0.79
0.34_oom
0.31
0.18
0.90-ao
0,40
CTGAN
0.94
0.92go0t
1.84
0.18 2ons
n.36
0.04gnos
0,96_am
0.36
NElow
2.95
0.91
0.77
0.01
0.31
0.03
0.85_mm
0.31
ARF
0.99
0.90
0.93
0.21 2.21
0.37 0.37
0.00
0.94-a02
0.46
TabDDPM
0.81
0.72.1024
0.44
0.21
0.40
1.24
TabSyn
0.91
0.83
0.58
0.21 0.21
0.40
0.07
0.97
0.61
TahDiff
g.93
0.87
0.63
0.24
0.37
0.39
0.97-am
2.61
TahFBM
0.98
0.96.am2
0.92
0.41
0.37
0.03
0.97-0m
0.42
NRGBoost
0.96
0.94
0.87 0,87 4000
0.21
0.23
=008
0.97-am
0.36
GReaT
g.95
0.91 1004
0.79
0.34_nmm
g.31
0.18
0.90_am
0,40
54

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Published as a conference paper at ICLR 2026
Table 50: Raw benchmark results of 13 tabular generators on "Nomao" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CT". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utilityy or local CT), while diffusion models typically excel at capturing global structure (i.e., global CI or global utility).
Density Estimation
Privacy Preservation DCR
MI. Efficacy Local utility
Structural Fidelity Global unility 1
Shape
Trend 1 c-precision
8-recall f
6-Presence
Der
g.00
1000
1.00
g000
g.00
g.00
1.00_am
1,00
SMOTE
g.70
0.99 .0m
0,98
0.77.0m
0.03 gnor
g.00
0.99
0,40
BN
0.77
0.93 0.93
0.95
0.21 0.21
0.15
0.00
0.72
0.38
TVAE
n.73
0.88
2000
0.13
g.05
0.06
0.96
=.67
GOGGLE
0.73
0.85
0.84
0.25
0. 0.11 1ase
1.58
0.72
0,26
CTGAN
0.68
0.89
0.92
0.02.000
0.06
0.07 0.07 20006
0.96-u04
2.19
NFlow
0.70
0.81 =omm
0.61
0.00=00:
0.20
5.97
0,55
0.05
ARF
0.74gam
0.76
0.98
0.07
0.04
0.15
0,96-amm
0.53
TabDDPM
2.64
0.75
0.45
0.16
0.18
2.77 3::45
0.72
0.60
TabSyn
0,58
0.72.2018
0.75
0.16
0.12gnm
7.12
0,95
0.60
TahDiff
0.74
0.78-011
0.80
2.166
0.10
0.48
0,95-006
0.68
TabEBM
0.74g00s
0.84_ons
0.94:005
0.18
0.26:0.0
0.47
0.95-00m
0,30
NRGBoost
g.73
0.86
a.78
0.16
g.09
1.92
0,95_am
0.17
GReaT
g.73gmm
0.85
0.84
0.25
0.11
1.58
0.
0,26
Table 51: Raw benchmark results 13 tabular generators on "Phoneme" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CI". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utility or local CI), while diffusion models typically excel capturing global structure (i.e., global CI or global utility).
Density Estimation
Privacy Preservation DCR
ML Efficacy Local utility
Structural F Fidelity Glohal millity 1
Shape
Trend 1 o- preciisin
8-recall f
6-Presence
D
1.00gam
1.00.am
1.00
.00
0.00
0.00
1.00
1.00
SMOTE
0.96
0.95
0.99+000
0.74
0.08
0.00
1.00-004
0.44
BN
0.97
0.98
0.98
0,98
0.46.omm
0.12
0.00
0.82
0.42
2.91
0.86
0.94
2.03
0.01
0.93-am
0.52:a22
GOGGLE
0.88
0.89
0.93
0.30
0. 0.14
0.37
0.79
0,27
CTGAN
0.79
0.89 0.89 100e
0.07 20m
0.19
0.45 gm74
0,90_a11
g.11
NElow
0.90
0.90
0.94
0.09
0.16gate
0.02
0.80_am
0.22
ARF
0.95
0.91 2002
0.99 20.0
0.22:00m
0. 2a0e
0.00
0.91 =001
0.67
TabDDPM
0.94
0.95-am
s:00
0.31
0.10
0.03
0.79
g.81
TabSyn
0.90
0.87
0.95
0.25
0.16
0.1 ga
0,88
0.71
TahDiff
0.92
2.91
0.96
0.22
0.18gnor
0.03
0,93_a10
2.39
TahFBM
0.94
0.92-amm
0.97
0.29
0.24
0.03
0.97
0.31
NRGBoost
0.94
0.93
+001
0.23
0.14:aas
0.03
0.96_am
0.21
GReaT
0.90
0.89.mm
0.86
0.22
0.19
0.12
0.71 0.71_n13
0.17
55

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Published as a conference paper at ICLR 2026
Table 52: Raw benchmark results of 13 tabular generators on "Plants" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CT". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utilitty or local CT), while diffusion models typically excel at capturing global structure (i.e., global CI or global utility).
Density Estimation
Privacy Preservation
MI. Efficacy Local utility
Structural Fidelity Global unility 1
Shape
Trend 1 c-precision
8-recall f
DCR 6-Presence
Der
1.00
1000
1.00
g.00
g.00
1.00_am
1,00
SMOTE
2.0
0.98
0.88 1,08
0.82
0.14
g.00
1.00-am2
g,45
BN
0.87
0.97 1007
0.26
0.15
0.00
0,89
0.29 0.29
TVAE
g.82
0.92.am
0. 2.80
0.20
0.25
0.08
0,95-00M
0.52:a.1
GOGGLE
0.84
0.94
0. 88 880
0.37
0.20 0.20
0.18 0.186
0,88
0.28
CTGAN
0.79
0.91
2002
0.89 0.89 s000
0. 0.24
g.20
0.20
0,95-um
2.19
NFlow
0.82
0.94_zomt
0.87 0.87
0.24
0.22
0.26
0,86
0.30=0.0
ARF
0.86:n01
0.94-am:
0.90 0.90
0.29 0.29
0. 1.19
0.02
0,93
0.57 0.57
TabDDPM
g.82
0.95.mm
0.78 0.78 1a:r
0.33
g.19
g.10
0.88 11
g.74
TabSyn
0.85
0.94
0.91
0.31 0.31
0.18
0.08 0.08
0,94_01
0.74gam
TahDiff
0.93.om
0086
0.25=a03
0.27
=.09
0,96-0015
0.68
TabEBM
0.07
0.96.oom:
0.94
0.35
0.30
0.05
0.97
0.28
NRGBoost
0.8
0.96gom
0.89 0.89 1000
0.27
g.19
2:005
0.97
g.22
GReaT
g.te
0,94
0.86
0.34
g.21
0.10g004
0,85_mm
0,24
Table 53: Raw benchmark results of 13 tabular generators on "QSAR" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CI". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utility or local CI), while diffusion models typically excel capturing global structure (i.e., global CI or global utility).
Density Estimation
Privacy Preservation DCR
ML Efficacy Local utility
Structural F Fidelity Glohal millity 1
Shape
Trend 1 o- preccision
8-recall f
6-Presence
D
1.00gam
1.00.am
1.00
..00..mm
0.00
0.00
1.00
1.00
SMOTE
0.76
0.96
0.95
0.76
g.08
0.01
0.93-a.11
2008
BN
0.77
0.98
0.98
0,98
0.54.om
0.12
0.00
0,78_n20
0.40
2.71
0.89
0.8 0,83
0.09=am:
a.15
0.10
0.85_a.1
0.47=a0m
GOGGLE
0.74
0.92
0.87 0,87
0.30.amm
0.14
0.24
0.70
0,26
CTGAN
0.64
0.86gom
0.89 0.89 100
0.04 20m
0.15
0.27 1.:s
0,85 0
0.12
NElow
0.72
0.91
0.85
0.052amm
0.16
0.10
0.66_gm
0.19 0.19
ARF
0.77
0.93
0.96
0. 0.15
0. a
0.01 =001
0.75
0.55
TabDDPM
0.71
0.93.om
0.71 0.71
0.25-a0m
g.08
0.22 2:26
0.70
a.70
TabSyn
0.75
0.92.mmm
0.92
0.26
0.15 1n01
0.08 1908
0.87 0.87
0.73
TahDiff
0.76gm0t
0.92.aut
0.90
0.20
0.22
0.07
0.89_a14
2n6
TahFBM
0.81
0.94.am
0.95+003
0.32-oos
0.27
0.04
0.91-012
0.30
NRGBoost
0.76
0.93.am
+aus
0.21=0m
0.17
0.04
0.90-a11
=.19
GReaT
0.71
0.91
0.76
0.20
0.17
0.17
0.66_a11
1.18
56

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Published as a conference paper at ICLR 2026
Table 54: Raw benchmark results of 13 tabular generators on ""SpeeDating" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CT". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utility or local CI), while diffusion models typically excel at capturing global structure (i.e., global CI global utility).
Density Estimation
Privacy Preservation DCR
MI. Efficacy Local utility
Structural Fidelity Global unility 1
Generator
Shape
Trend 1 c-precision
8-recall f
6-Presence
Der
1.00
1000
1.00
0000
g.00
g.00
1.00_am
1,00
SMOTE
2.95
0.94.om
0,96
0.78
2.14
g.00
1.02
2.44
BN
0.95
0.95 2.9
0.97 10:0
1000
0.28
g.3e
0.01 g000
0,83
0,36
TVAE
g.90
0.86
+.91
0.07
0.34
0.01
0,98_0015
0.52:a00
GOGGLE
0.88
0.87
0.87 0.87
0.28
0. g.25
0.24
0,83_0011
0,25
CTGAN
g.85
0.84
0.92
0.04
0.26
0.23
0,93
0.13
NFlow
0.86.a01
0.84_aom
0.75
0.05=000
0.25
0.15
0.81 0,81=0.0
0. 0:13:0008
ARF
0.92
0.89
0.90 0.90
0.24-000
0.23 20.0
0.06
0.92-amm
a.56
TabDDPM
n.8
0.71 0.71
0.24
0.23 10004
g.31
0.84_a.m
0.72
TabSyn
0.86
0.83
0.86
0.21 0.21
0.27
0.09
0,93
0.69 2000
TahDiff
0.86
0. +.08
0.19
0.30
0.14
0,96-008
0.67
TabEBM
0.93
0.91
0.95
0.27
0.33
0.02
0.98-006
0,30
NRGBoost
0.90.am
0.87 1,006
0.19
p.22
0,04
0.97-am
0.18
GReaT
2.87
0.84
0.24
g.27
0.12gn00
0.80_a
g.20
Table 55: Raw benchmark results of 13 tabular generators on "Splice" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CI". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utility or local CT), while diffusion models typically excel capturing global structure (i.e., global CI or global utility).
Density Estimation o- preciisio
Privacy Preservation DCR
ML Efficacy Local utility
Structural F Fidelity Glohal millity 1
Shape
Trend 1
8-recall f
6-Presence
D
1.00
1.00.am
1.00
..00..mm
0.00
0.00
1.00
1.00
SMOTE
0.98
0.97
0.98
0.88
0.00
0.00
1.01
0.47
BN
0.99
0.95
0.93
0.34
0.64
0.04
0.69-a22
0.19 0.19
2.95
0.92.amm
0.8 0089
0.56=omm
0.83
0.03
1.00-004
0.48
GOGGLE
0.94.am2
0.90.aom
0.83
0.49..m
0.50
0.08
0.64_n22
0,30
CTGAN
0.94
0.90
0,94
0.43 0.43 2mm
0.67 gnos
0.03gno4 goos
0.99_ams
0.24
NElow
g.85
0.77
0.70
0,21
0.64ga07
0.04
0.47-mmn
0.31
ARF
0.99
0.95
0.91 +001
0.45
0.91 2aue
0.01 =200
0.78=a.0
0.21 2a.5
TabDDPM
g.95
2.92
0.70
0.38
0.61
0.06
0.54_020
0.60
TabSyn
0.85 1n11
0.77
0.54
0.32
g.57
0.35 g045
0.93
0.66
TahDiff
g.87
0.80
0.56
0.31
0.58
0.39
0,88_a11
0.65
TahFBM
0.96
0.93.am
0.94
0.59
0.26
0.01
0.98-aum
0.35
NRGBoost
0.92
o.88
0.82+a.00
0.38
0.28
0.04:a08
0.97-am
GReaT
0.94
0.90
0.83
0.49.nmm
0.50
0.08
0.64_a22
1,
57

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Published as a conference paper at ICLR 2026
Table 56: Raw benchmark results of 13 tabular generators on "Vehicle" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CT". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utilitty or local CT), while diffusion models typically excel at capturing global structure (i.e., global CI or global utility).
Density Estimation
Privacy Preservation DCR 6-Presence
MI. Efficacy Local utility
Structural Fidelity Global unility 1
Shape
Trend 1 c-precision
8-recall f
Der
g.00
1000
1.00
g000
g.00
g.00
1.00_am
1,00
SMOTE
2.95
0.97
0,96
0.86
g.12
g.01
0.98
g.41
BN
0.96 0,94gmm
0.97
0.33
0.17
0.01 0.01
0.64
0.28
TVAE
g00r
0.86
+000
0.08
2.39
0.16
0.84
2035
GOGGLE
0.89
0.91 =o.
0. 88
0.30
0.22 0.22
0.07
0.59-0.19
0.23
CTGAN
0.78gme
0.90
0.82
0.02.g0mt
g.24
0.13
0.82-g019
0.08
NElow
0.88
0.85
0 0.89
0.00=0m:
0.24
0.13
0.46
a.09
ARF
0.94
0.93
0.96::01
0. 0.16::022
0.17
0.01 1:000
0.84_004
0.43
TabDDPM
0.85 1no
1.90
0.77 0.77 10.1
0.28 1om
0.14
g.04gaos
0.62
0.72
TabSyn
a.te
0.93
0.92
0.27 0.27
2.20
0.04
0,88
0.74g006
TahDiff
2.88
0.87=amm
0004
0.18
0.31
0.07
0.84
0.62:204
TabEBM
0.91 0.01
0.94.oo:
0.93
0.40
0.36
0.04
0.93
0,28
NRGBoost
0.88 0o8s gm9
0.88 1000
0.18 2011
0.26
g.12
0,88
0.15
GReaT
g.85
0,87
0.75
0.18
0.27
0.20
0.49_
0.15
Table 57: Raw benchmark results of 13 tabular generators on "Zernike" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CI". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utility or local CI), while diffusion models typically excel capturing global structure (i.e., global CI or global utility).
Density Estimation
Privacy Preservation DCR
ML Efficacy Local utility
Structural F Fidelity Glohal uillity 1
Shape
Trend 1 o- preccision
8-recall f
6-Presence
D
1.00
1.00.am
1.00
1.00..mm
0.00
0.00
1.00
1.00
SMOTE
0.97
0.98-cmm
0.90
0.90-o0m
0.20
0.00
0.98-a00
0.31 2a32
BN
0.97
0.98 0.98
0,96
0.72
0.18
0.00
0,54
g,31
0.87
0.93
0.76
0.03
0.47
0.31
0,90=a0x
0.38
GOGGLE
0.90
0.94-oom
0.79
0.31
0.35
0.18
0.42
0.18
CTGAN
g.me
0.95
0.65 1ov0
0.00 0.00 201
0.40
0.03 goos
0,82_m
0.06_am
NElow
0.90
0.87
0.77
0.00
0.41
0.80
0.14_am
0.01 100t
ARF
0.96
0.94-am
0.87 0.87 #001
0.01 =001=00:
0.40
0.01 0.01=000 20000
0.77=004
0.21 =aot
TabDDPM
0.68
0.92.am
0.44
0.19-
0.51
0.21
0.30
0.62:a01
TabSyn
0.92
0.96
0.96
0.83 0.83
0.24
0.36
0.09
0.84
0.70
TahDiff
g.91
0.92.mm
0.77
0.192020
0.40gnte
+0077
0.82_a21
2.61
TahFBM
0.94
0.96
0.91 0.91
0.40-zom
0.37
0.08
0.92-m10
0,23
NRGBoost
0.95
0.94
0.89+aa5 +00s
0.19==020
0.35
0.16:a.44
0.90-a.11
0.13
GReaT
0.84
0.91
0.55
0.19
0.29
0.56
0.29_na3
0.11
58

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Published as a conference paper at ICLR 2026
F.2.2 REGRESSION DATASETS
Table 58: Raw benchmark results of 13 tabular generators "Ailerons" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, SMOTE generally achieves the highest performance in capturing local structure (i.c., local utility or local CI), while diffusion models typically excel capturing global structure (i.e., global CI or global utility).
abbreviate "conditional independence" as "Cr".
Density Estimation
Privacy Preservation DCR 6-Presence
ML Efficacy Local utility
Structural Fidelity Global utility 1
Generator
Shape
Trend f c-precision
9-recall f
1.00
1.00
1.00
1000
g.00
0.00gaco
1.00gam
1.00
SMOTE
gm7
0.99
2.90
g.85
0.01
0.00gaco
0.88_aa1
g.35
BN
0.78
pm96
0.94
0. 0.03
0.05
2002
0.00
0,56-035
0.51 20:8
TVAE
0.70
0. 0.86
0.28
g.00
0.18
0.76_am
0,46
GOGGLE
0,57
0.90
0.53
0.19
0.05 g004
1.61
0,80
0,18 0.18
0.682am
0.96.am
+.91
0.09
2.02
0.06
0.75
NElow
0.68
0.8
0.63
0.00.000
0.12:0.10
0.94
0,51
0,05
ARF
gm7e
0.98.am
0.95 0,95 1,00
0.22
0.03 1000
g000
0,64_035
g.18
TahDDPM
0.72
0,94-amz
0.84
0.30
a.02
0.09
0.52_a53
2.
TahSyn
0.52
0.90
0.60
0. 0818
0.17
3.088
0.81
0.642032
TabDiff
0.76
0,97-20m2
0.87
0.22::0.6
0.07
0.09
0.87=020
2.71
TabEBM
0.76
0,96
0.93
0.22:
0.07
0.09
0,57 0,57
0.43
NRGBoost
2.68
0,92.001
0.53
0.18
0.22
2.39
0.79_022
0.18
GReaT
0,94
0.67
0,20
0.07
0.97
0.3
0,20
Table 59: Raw benchmark results of 13 tabular generators on "California" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CT". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utility or local CT), while diffusion models typically excel at capturing global structure (i.e., global CI or global utility).
Density Estimation
Privacy Preservation DCR
ML Efficacy Local utility
Structural Fidelity Global utility 1
Generator
Shape
Trend 1
c-precision
3-recall f
6-Presence
Dest
1.00
1.00.am
1.00
1.00...m
0.00
0.00
1.00..0m
1,00
SMOTE
0,98
0.99
0.99
0.78
gnze
0.00
0.96_mms
2.44
BN
0,98
0.97
0.98
0.44
g.04
0.00
0.73
0,72
a.94
0.91 =am
#000
2.23
2.07
0.1 0.10:a0e
=0.12
0.53=024
GOGGLE
0.7
0.83
0.72
0.21
0.08
2.75
0.80
0,14
CTGAN
1.93
0.18 200
0.03 gmo
0.15 0.15 gm
0,84_017
0.16
NElow
0.89
0.86
0.90
0.08
0.1 2.12
0.33
0.45
0.06
ARF
0.97=a00
0.87
0.99 0.99
0. 0.26==0m
0.05
0.00
0.69-024
0.68
TabDDPM
0.93
0.94-am
0.94
0.42.c0m
0.04
0.04
0.60-a23
a.79
TabSyn
0.95
0.94
0.92
0.40
0.06
0.39
0.88
0.78
TabDiff
0.94gmm
0.90
0.96
0.28
g.09
0.04g304
0,88_a13
0.75
TahEBM
0.93
0.92
0.97
0.24
0. 0.11
0.04
0.62-018
0.47
NRGBoost
0.93
oo8
0.94
0.23
0.05
0.05
0,77=a30
0.15
GReaT
0.88
0.88
0.87
0.22
0.12
0.10
0.49_aa3
0,16
59

---

Published as a conference paper at ICLR 2026
Table 60: Raw benchmark results of 13 tabular generators on "Elevators" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CT". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utilitty or local CT), while diffusion models typically excel at capturing global structure (i.e., global CI or global utility).
Density Estimation
Privacy Preservation
MI. Efficacy Local utility
Structural Fidelity Global unility 1
Shape
Trend 1 c-precision
8-recall f
DCR 6-Presence
Der
1.00
1000
1.00
2000
g.00
g.00
1.00_am
1,00
SMOTE
0.85 10o1
0.99 10m
0.95 1000
0.81
g.00
g.00
0.92
0,39
BN
0.87
0.96
0.96
0.28
0.05 g000
0.00
0,64_a17
0.61
TVAE
g.82
0,94
+.91
0.25
g.05
0.14
0.78
0,50
GOGGLE
0.64
0.87-2om
0.63
0,20
0.06
2. 2.18:0551
0,80
0,16:000
CTGAN
0.79
0.942000
0. 0.94
0. g.04
0.02
0.1 12007
0.79
0.14
NFlow
0.78gam
0.88-
0.77
0.04-00
0. 0.12
0.64
0,48
=.05=a01
ARF
0.93
0.97 1:000
0.24-00:
0.04
0.00
0.67=
0.63
TabDDPM
n.82
0,94_nmm
0.89 0.89 10/0
0.36
0.03 gaoe
0,07 1005
0.56_gm
g.74
TabSyn
0.74
0.92.amm
0.76
0.29
0.11
1.73
0,84_
0.71
TahDiff
0.85
0.93.m
0.91
0.25
2.08
0.06
0.87=001
0.73=0.2
TabEBM
0.84
0.94.om:
0.95
0.23
0.09
0.07
0.59-00
0.45
NRGBoost
0.91.om
0.74
0.21
0.14gam
0,22
0.78-
0.17
GReaT
0.78
2091
0.77
0.21
0.10
0.54
0.49_mm
0.18gam
Table 61: Raw benchmark results of 13 tabular generators on "H16" dataset. We report the normalised mean + std metric values acToss datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CI". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utility or local CI), while diffusion models typically excel capturing global structure (i.e., global CI or global utility).
Density Estimation
Privacy Preservation DCR
ML Efficacy Local utility
Structural F Fidelity Glohal millity 1
Shape
Trend 1 o- precision
8-recall f
6-Presence
D
1.00gam
1.00.am
1.00
1.00..mm
0.00
0.00
1.00
1.00
SMOTE
0.88
0.99
0.95
0.83
0.05 20.00
0.00
0,98-a02
0.45
BN
0.89
0.99.nm
0.99
0.99 0.991000
0.61.oom
0.03 ioo
0.00
0,80_a23
0.80
0.98
0.94+002
0.29-00:
10
0.35
0.86=am
0.62:aa2
GOGGLE
0.68
0.95
0.61
0.23
0.08
6.50
0.86
0,20
CTGAN
0.97 1.9
0.97 0.97 1000
0.22gam
0.05 gate
0.07 1.00
0.87 10
0.20
NElow
0.83
0.94-am
0.86
0.07
0. 0.11
0.07
0.57_a11
0.10
ARF
0.90)=00
0.98
0. 0.94+000
0. 0.19-00m
0.06
0.00
0.74-020
0.70
TabDDPM
0.83
0.96
0. 0.89 2007
0.40-:0ms
0.04ga0
0.05 2007
0.65-a17
0.77
TabSyn
0.69
0.78 gmmm
0.24
0.10
3.88
0.85
0.67
TahDiff
g.85
0.96
0.89
0.24
0.20
0.13
0.87
0.71
TahFBM
0.87
0.97
0.96
0.26
0.16
0.06
0.64_021
0.50+am5
NRGBoost
0.87
0.95-am
0.94
0.24
0.07
0.23
0.82_a22
0.17
GReaT
0.77
0.95
0.88
0.25
0.12
0.72
0.58
g,21
60

---

Published as a conference paper at ICLR 2026
Table 62: Raw benchmark results of 13 tabular generators on "Liver" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CT". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utilitty or local CT), while diffusion models typically excel at capturing global structure (i.e., global CI or global utility).
Density Estimation
Privacy Preservation DCR 6-Presence
MI. Efficacy Local utility
Structural Fidelity Global unility 1
Shape
Trend 1 c-precision
8-recall f
Der
1.00
1000
1.00
g000
g.00
g.00
1.00_am
1,00
SMOTE
0.90
0.97
1.90
0.81
g.01
0,43
BN
0n
0.96
0.94
0.54
0.23
0.01 g.01
0.91 0,91
0,76
TVAE
n.77
0,91 =omm
0.50
0.47=003
0.18
0.12
0.97=0um
0.72
GOGGLE
0.65
0.90
0.77
0.37
D. 0.18
0.17
0.94_0.13
0,28
CTGAN
n.49
0.87
0.61 20.17
0. 0.16
g.29
0.37 0.37 2:277
0,95-011
2.19
NFlow
0.88
0.92.s0m2
0.93
0.47=005
1.140
0.02=0001
0.86
0.
ARF
0.00
0.96
0.88 1:005
0.48
0. 1.18
0.01 0.01
0,93
0.81 20.8
TabDDPM
n.84
1.93
0.88 1o/6
0.54
0.13
g.06g
0.87_m.0
0.77
TabSyn
0.86
0.95
0.89
0.55
0.17
0.05
1.00
0.80
TahDiff
0.86
0.96.am
0.87 +007
0.49=0m
0.20
0.05
1.00
0.11
TabEBM
0.86
0.94.om:
0.89
0.65
0.13
0.06:005
0.93-005
0.61
NRGBoost
0.85 Lome
0.91.om
0.88 1oor
0.52
0.15
0,06
0,98-m0
g.37
GReaT
0.78
0,93
0.81
0.46
0.17
0.08
0.87
0.36
Table 63: Raw benchmark results of 13 tabular generators on "Sales" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CI". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utility or local CI), while diffusion models typically excel capturing global structure (i.e., global CI or global utility).
Density Estimation o- preccision
Privacy Preservation DCR
ML Efficacy Local utility
Structural F Fidelity Glohal millity 1
Shape
Trend 1
8-recall f
6-Presence
D
1.00
1.00.am
1.00
..00..m
0.00
0.00
1.00
1.00
SMOTE
0.80
0.96
0.97
0.79 =0.0
0.03 s0.0
0.00
0.97-0m4
0.39
BN
0.79
0.89.am
0.89
0.94
0.29
0.22 100e
0.01 g,01
0,58 0,58_n22
0.59 0,59
0.73
0.87=am
#000
0.27=00:
0.25
0.03
=0.12
0.62-2022
GOGGLE
0.57
0.81
0.68
0.24
0.18
12.17
0.80
0.22
CTGAN
0.71
0.89
0.95 1.95
0.26_mmm
g.11
0.04
0,83_m17
g,25
NElow
0.73
0.84
0.87
0.24
0.17
0.07
0.43
0.14
ARF
0.75
0.89
0. 0.85
0.38
D. 16
1,38
0.57 0.57=022
0.62
TabDDPM
0.66
0.84_oos
0.47 s::49
0.24
0.24
3.40
0.42-n28
0.60
TabSyn
1.78
0.91
0.96
0.34
0.16gnos
0.02
0.90
0.78
TahDiff
0.78gmt
0.91gam
0.96
0.33
0.15
0.02
0.90_a11
e020
TahFBM
0.77
0.89
0.91
0.31
0.13
0.64
0.66--112
0,50+a.0
NRGBoost
0.70
0.84.am
0.56:a440
0.27=
0.23
0.15
0.72-a37
0.18:
GReaT
2.75
0.89.om
0.85
0.38
0.16
1.38
0.51_nas
1,27
61

---

Published as a conference paper at ICLR 2026
Table 64; Raw benchmark results of 13 tabular generators on "Space" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CT". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utilityy or local CT), while diffusion models typically excel at capturing global structure (i.e., global CI or global utility).
Density Estimation
Privacy Preservation DCR 6-Presence
MI. Efficacy Local utility
Structural Fidelity Global unility 1
Shape
Trend 1 c-precision
8-recall f
Der
1.00
1.00
1.00
g000
g.00
0.00
1.00_am
1,00
SMOTE
0.98
0.99 10m
0,98
0.78
0.08
g.00
0.96_.04
0.42
BN
0.98
0.99
0.97 1001
0.57 0.57
0.14
0.00
0.79
0.92
TVAE
n00
0.90.amm
0.85
0.11 0.11
0.20
0.23
0.75
0.40
GOGGLE
0.72:a01
0.88
0.72
0,21
D. 1,144004
1.91 +237
0.82=021
0.15
CTGAN
0.77
2.93
0.77 a0.10
0.05 0.05
0.20
0.21 2:223
0,80
0.08
NElow
0.89
0.89.am2
0.91 0.91 +0.05
0.09_
0. 0.15
0.04
0.57_0.0
0. 0.11
ARF
0.97
0.98
0.98
0.32:00m:
1010000
0.00
0,73
0.73
TabDDPM
0.96.mm
0.94
0.38
g.09
0.05 1006
0.65
g.80
TabSyn
g.93
0.97
0.94
0.35
0.15
0.04
0.89
0.79
TahDiff
0.97.am2
0.94
0.34=000
2.13
0.04
0.89_
0.78=022
TabEBM
0.94
0.95
0. 0.94:003
0.32:s0.0
D. 0.14game
0.04
0.67
0,47
NRGBoost
g.03
0.87
100t
0.21
0.20
0.40
0.84_m11
0.16ga21
GReaT
0,91
0.82
0.27
0.15
0.12
0,57_014
0.17g021
Table 65: Raw benchmark results of 13 tabular generators on "Superconductivity" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CI". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utility or local CI), while diffusion models typically excel at capturing global structure (i.e., global CI or global utility).
Density Estimation
Privacy Preservation DCR
ML Efficacy Local utility
Structural Fidelity Glohal millity 1
Shape
Trend 1 a- preccision
8-recall f
6-Presence
D
1.00gam
1.00.am
1.00
..00..mm
0.00
0.00
1.00
1.00
SMOTE
0.95
1.00
0.99
0.45
0.01 20:00
0.00
0.97-0m
0.41
BN
0.96
0.99
0.99.am
0.99 1009
0.16
0.07
0.00
0.72
0.85 0.85
a.89
0.94
0.91
0.00=am:
0.35
0.04
0.73
0.42:aa34
GOGGLE
0.86
0.94_o04
0.82
0.17
0.26
2.10
0.82
0,20
CTGAN
n.86
0.95
0.85 1005
0.00 201
gn38
0.76_024
0.05
NElow
0.87
0.84-aot
0.63
0.00
0.50
4.94
0.32_nm
0.01
ARF
0.95
0.99:am
0.96
0.02=000:
0.18
0.00g
0.64-026
0.54
TabDDPM
0.66
0.90
0.45
0.12::012
0.14g000
2.46
0.40-a21
0.62:aa2
TabSyn
0.91
1.97
0.97
0.91
0.12
0.23 100e
0.33
0.85_m11
0.73
TahDiff
g.93
0.97
0.93
0.13
0.24gnot
0.33
0.85_a16
0.75
TahFBM
0.92=am0
0.97-am
0.93
0. 0.12.20.2
0.184006
0.33
0.47-022
0.37=a.0
NRGBoost
0.93
0.89.am
0.75
0.12.20.2
0.31
4.29
0,74_a32
0.12
GReaT
0.90
0.95
0.86
0.19..om
0.23gamm
1.15
0.48_na:
0,22
62

---

Published as a conference paper at ICLR 2026
Table 66: Raw benchmark results of 13 tabular generators on "Wine" dataset. We report the normalised mean + std metric values across datasets. We highlight the First, Second and Third best performances for each metric. For visualisation, we abbreviate "conditional independence" as "CT". SMOTE generally achieves the highest performance in capturing local structure (i.e., local utility or local CI), while diffusion models typically excel at capturing global structure (i.e., global CI or global utility).
Density Estimation
Privncy Preservation DCR
MI Efficacy Local utility
Structural Fidelity Global utility 1
Generator
Shape
Trend 1
c-precision
3-recall f
6-Presence
Peet
1.00
1.00.am
1.00
1.00.am:
g.00
0.00
1.00-a00
1.00
SMOTE
2.97
0.99
0.94
0.67
0.08
g.00
0.98_mmr
0,44
BN
0.97
0.93
0.96
0. 0.18
a.22
0.01 0.01
0.78
0.49
2.89
0.95.amm
0.78
2.23
=0.10
0.88_
0.48
GOGGLE
0.72
0.92-1o44
0.63
0.18
0.26
1.49
0.87
0.12:a.9
CTGAN
0.97.am
0.95 0.95 1001
0.16
0.13 1oos
0.03 2005
0,92_mm
0.17
NElow
0,9
0.92
0.10
0.16gnte
0.04
0.70
2.08
ARF
0,96.a00
0.98.a0
0.97 0.97 #001
0. 0.22
0. 2
0.00
0.81 0.81
0.66--221
TabDDPM
0.93
0.97
0.93
0.29
0.09
0.02
0.76
0.75
TabSyn
0.93
1.97
0.95
0.28
0.16
0.01 g,00
0.93-amm
0.76
TabDiff
g.94
0.98_mm
0.96
0.27
0.16gno4
g.01
0.93_mm
0.76
TahEBM
0.94_am
0.97
0.95
0.26
0.17
0.01 0.01
0,80
0.45
NRGBoost
0.94
0.93
0.91
0.20
0.13
0.02=a01
0.90-ao11
0.14
GReaT
0.86
0.92.004
0.71
0.21
0.19
0.36
0.
g.13
63


Reviews:
[{"review_id": "ADpvGKWJQY", "reviewer": "Reviewer_njCP", "summary": "The paper proposes a benchmark framework to assess methods for generating synthetic data based on existing datasets. The main novelty is that it introduces a metric to measure structural fidelity based on a global utility score without the need for ground-truth causal graphs. This enables the study of structural fidelity for real-world data where such graphs are typically unavailable. In empirical experiments, they first demonstrate a high correlation between the new metric and existing metrics on synthetic tasks (where the ground truth is available) and then assess the performance of different generators on real-world tasks.", "questions": "[clarification] Would reaching a utility score >1 be possible?\n\n[clarification] What is the size of the generated dataset D_synth with respect to D_ref? I assume they are the same size, but it might also be interesting to analyze how the proposed metrics behave for larger or smaller synthetic datasets relative to the reference data.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "**Novelty** The paper introduces a new metric that complements the assessment of data generators on real-world tasks\n\n**Clarity** I enjoyed reading the paper as it is straightforward, with a good structure\n\n**Impact** Studying tabular generators is a very relevant task for a broader audience at ICLR and a much-needed research direction directly related to developing better foundation models for tabular data", "weaknesses": "**Aggregation of Metrics** I understand the importance of aggregating metrics to provide concise and interpretable results. However, a considerable amount of information may be lost in the aggregation process. It would be valuable to include some indication of the variability or distribution of utility scores across features. For instance, are there notable outliers where the generator fails to capture feature usefulness, or are all features consistently represented? Such an analysis could strengthen the empirical insights.\n\n**Readability** (This did not influence my rating, as it is straightforward to address.)\nThe paper employs multiple text styles (boldface, italics, color) without a clear or consistent rationale. For example, in lines 117-131, it is unclear why certain words are boldfaced. Similarly, the colored text and structure of (the huge) Table 2 do sufficiently aid visual comprehension or highlight the key messages. For example, consistent colors for the Top-3 and Bottom-3 results would help visualize similarities across columns. Moreover, showing real-world and SCM results for each metric side-by-side would support following the content of Section 4.2.\n\n**Ethics Statement** This is not an ethics statement but a summary/conclusion.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "1FyFqaqft1", "reviewer": "Reviewer_7rse", "summary": "The paper proposes a comprehensive benchmark for evaluating tabular generative models. It identifies a key gap in existing evaluation measures and proposes new metrics to address this issue. While most evaluation metrics focus on dimensions such as density estimation, privacy preservation, or machine learning efficiency, these metrics are not tailored to assess whether synthetic data preserves the underlying structural (causal) relationships among variables. To address this, the paper proposes a new evaluation dimension called structural fidelity, and a new metric, global CI, to measure this new dimension.  Because, this metric requires knowledge about the underlying structural causal model (SCM), which is almost always unknown for real datasets, the paper also introduces a SCM free heuristic metric, global utility, which correlates strongly with global CI and can be used as a proxy to measure structural fidelity.  \n\nThe paper performs extensive evaluations using 13 tabular generators across 29 datasets (including both expert-validated causal and real-world datasets) and provides many interesting insights about the performance of popular tabular generators and of the evaluation metrics.", "questions": "Some of the benchmark datasets are very large (e.g., Higgs, and SCM datasets). How did the paper handle the TabPFN model in situations where the evaluation dataset had more than 10,000 rows? Was TabPFN removed from the predictor’s ensemble in these cases? (My understanding is that the current version of TabPFN can only handle datasets with up to 10,000 rows.)\n\nThis is only a suggestion, that the paper might find useful for future work. In Table 2, in addition to the 13 generators, the paper includes the reference (training) data, $D_{ref}$, for direct evaluation. This helps better ground the interpretation of the scores achieved by the generators, showing that the metrics can distinguish between high- and low-quality data.  But, perhaps, another interesting comparison would be to include direct comparisons not only to the reference set but also to a separate independent set (of the same size as the reference set) from each dataset (which is not touched during training). Since the independent set, $D_{indep}$, is by construction independent and identically distributed to the reference set, it could be used to estimate the performance of an ideal generator, truly capable of generating independent samples from the same distribution as the reference data. \n\nHaving these comparisons would potentially provide complementary information for the $D_{ref}$ direct evaluations. For instance, in the case of privacy metric such as the DCR, while $D_{ref}$ will produce a score equal to zero, $D_{indep}$ would estimate the median DCR score we would expect to see in an ideal generator. This would represent a baseline value and sort of “ground truth” value the generators should be aiming to. (While low DCR values indicate low privacy, high DCR scores are not necessarily a good thing either, since they usually indicate low data fidelity.) Additionally, the direct evaluation of $D_{indep}$ could also be potentially used to check when models are generating data that is too close to the training set (e.g., when a model is generating data $D_{syn}$ with better fidelity scores than $D_{indep}$). \n\nTo generate this independent set the paper would need to change its current data split and re-split the full dataset of each benchmark into a test set, a validation set, a training (reference) set, and a independent set of the same size as the training set. While this would require re-running all the analyses in that paper (what is certainly not feasible during the short discussion phase) perhaps the paper might want to consider implementing these comparisons in the future, as they might provide additional insights (and the paper aims for TabStruct to be an ongoing effort aiming to continue to evolve). \n\nMinor suggestions:\n\nLine 1515: “TarStruct” -> “TabStruct”", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "The paper addresses the very important (and difficult) problem of evaluating the performance of tabular data generators.\n\nIt identifies a blind spot (structural fidelity) in the current evaluation metrics and proposes new metrics to measure it.\n\nThe experimental setup is as rigorous as it gets.\n\nThe very careful and detailed analyses of both the different generators and the different metrics provide corroboration to many observations in previous studies, as well as several new and valuable insights. \n\nThe paper provides a very thorough discussion of the limitations of the proposed metrics. \n\nThe framework’s modular design allows researchers to easily plug in new datasets, generators, and metrics, making it a great resource to the synthetic tabular data generation community.", "weaknesses": "The one point I think is missing from the paper is a comparison against the detection test metric (C2ST), which measures data fidelity by evaluating the discriminating ability of classifiers trained to discriminate between synthetic and real data. C2ST is a very popular metric, widely used in the field, which also aims to measure fidelity at a full dataset scale.  \n\nGiven the large scale of the experiments presented on the paper, I understand that it would likely be difficult to include extensive comparisons during the short time frame of the discussion window. However, I think the paper would benefit from providing at least some preliminary comparisons of C2ST against the proposed global utility metric.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "yzBFxScRfc", "reviewer": "Reviewer_mx31", "summary": "The paper addresses the problem of evaluating tabular data generators. The paper argues that the existing benchmarks are insufficient because they either neglect the structural properties of the tabular data, or are biased towards downstream task performances, and are often limited to toy examples where the causal graph is known.\n\nThe paper proposes to incorporate structural fidelity as a core evaluation dimension, and introduces a metric called, \"global utility\", which is an SCM-free metric for assessing structural fidelity. A comprehensive benchamark \" TabStruct\" is proposed to evaluate 13 generators across 29 datasets including real-world and SCM-based data.", "questions": "1. Could you elaborate on the theoretical gap between high global utility and the preservation of the Markov equivalence class? Are you aware of any hypothetical data-generating processes where a model could achieve high global utility while  violating key conditional independencies? How likely is this to happen in practice?\n2. The high correlation between the global utility and the global_CI is taken as the validation of the global utility; but, the global_CI score is an imperfect ground truth because  the CI test have limitations themselves. So how does this inherent noise and potential inaccuracies of the CI-based ground truth affect your confidence in the correlation values and the conclusions you draw from it?\n3. global utility is normalized by the performance on the reference data. How does this metric behave in low-data regimes? What is the relationship between the reliability of the global utility and the size and quality of the reference dataset?\n. How does the computational cost of global utility scale with the number of features?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "+ the proposed problem is highly relevant. The paper identified a significant gap in the evaluation of tabular generative models and moves beyond simple ML efficacy (performance on downstream tasks) and density estimation\n+ the proposed metric is novel (global utility) and interesting. \n+ the empirical validation is rigorous and comprehensive with 13 generators from 9 categories and 29 datasets. It is also commendable that the authors chose some challenging datasets where the models don't easily achieve perfect scores.\n+ Tabstruct library is a valuable open-source contribution", "weaknesses": "- The global utility metric is a heuristic proxy, not a formal measure. Although the paper provides strong empirical evidence it is important to acknowledge that it is a proxy. Although it is acknowledged in the paper, it should probably be emphasized more. \n- The metric measures \"predictability\" rather than the \"causal structure\". A generative model could learn powerful but spurious correlations that allow for excellent cross-prediction of variables. This would make it score high on global utility, but be structurally unfaithful.\n- The \"full-tuned\" configuration of the global utility metric requires training an ensemble of predcitors for each of the columns in the dataset. That is computationally expensive, especially for high-dimension data. Although the \"tiny-default\" is much faster and seems to be stable ranking wise, the fundamental approach is very expensive and this could lead to scalablity issues in practice.\n- The finding that the BAyesian networks and GOGGLE perform poorly on structural fidelity metrics is counter-intuitive. Although there is some explanation in the paper, this should probably be probed more deeply. Where is the failure happening?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "KWyO8ZLbnP", "reviewer": "Reviewer_AASQ", "summary": "The paper proposes a benchmarking framework including a novel metric for tabular data generators. The benchmarking framework is applied to 29 tabular SCM-based or real-world datasets and 13 generators.\n\nThe work has several contributions:\n* A good motivation for introducing yet another benchmark for tabular data generators.\n* A novel way of assessing the performance of data generators, based on structural fidelity, inspired by a causal perspective.\n* A benchmarking framework with datasets, generators, and the evaluation pipeline. \n* Many insights into existing failure modes and strengths of tabular data generators. \n* An extreme commitment to reproducibility and scientific rigor in code and all parts of the paper. \n* A detailed and extended overview of related work for all parts of the work, from motivation to benchmark to insights.", "questions": "* Using SCM-based datasets to benchmark tabular data generators is well motivated. Yet, it is hard to tell if datasets, for example, about physical laws, are representative of real-world tabular data. Real tabular data is often noisier than datasets we have / can get from data with a ground-truth SCM. Thus, it is hard to predict how useful and representative the subset of SCM-based data will be for TabStruct in the future to guide generator development. Have the authors considered ways to get more such data or more realistic data? For example, priors of tabular foundation models such as TabPFN often use SCM-based data for pretraining that might be more realistic. Likewise, they usually add noise to the SCMs' data. \n* A core use of SCM-based data could be, as mentioned, to check for extrapolation instead of interpolation. This would also point to potentially benchmarking an entirely new kind of generators, that is, generators that can generate non-IID data. This would be akin to model benchmarks for non-IID data, e.g., https://arxiv.org/abs/2406.19380, rather than purely IID data, e.g., https://arxiv.org/abs/2506.16791. Given this comparison, TabStruct and the SCM-based data could enable benchmarks for non-IID data generators, and the Global CI would be appropriate for this. At the same time, Global utility might need to use non-IID models/validation splits. Was this intended by the distinction of interpolation vs extrapolation in Figure 1? And how does this framing position the current benchmark? \n* The current formulation of the Global utility metric utilizes a binary output of the CI test. While theoretically well motivated, I was wondering if a more continuous output of the CI test might not be better suited. For example, one could return the alpha value at which the test fails, rather than 0/1. Then, the \"decision boundary\" of the Global utility would be smoother. Moreover, it would be more similar to the smoothness of global utility (which averages over continuous values) and maybe provide a higher correlation. Or, one could use a similar significance test in global utility, such as a Wilcoxon test at alpha 0.01 to test if Perf(D_ref) is equal to Perf(D) over samples or bootstraps. \n* Why was balanced accuracy chosen as a metric for classification tasks? It is well established in model benchmarks that metrics such as ROC AUC for binary and log loss for multiclass classification are more appropriate for comparing models (e.g., see https://arxiv.org/abs/2506.16791 and its cited/related benchmarks and https://pages.cs.wisc.edu/~dpage/cs760/roc.pdf). I think here, a non-threshold-based metric would also be more appropriate. The impact of this choice might be less severe because AutoGluon was used, which, if optimized for balanced accuracy, should have employed threshold tuning by default (as required for evaluation for balanced accuracy). Do you know if threshold tuning was used in your experiments? On that note, the current formulation could also create some numerical problems for outliers where RMSE approaches 0. It might be worth improving the implementation with safeguards against numerical issues when computing relative metrics. \n* The description of nested validation in Line 314 is very hard to parse, in my opinion. The appendix and text make it clear enough later. But the work could benefit from shortly introducing the validation method in the first sentence of the paragraph. I think in this case, a nested repeated shuffle split would be one way to describe it (?).  Furthermore, is stratification used for splits for classification datasets? If not, this might be important for imbalanced classification datasets in the future. \n* How does the framework control randomness and seeds of the methods, data splits, and tuning?\n* The correlation analysis in Section 4.1 is nice and insightful, but it remains unclear if the correlation is high enough to be representative enough for a good benchmark. There might be ways to test or verify that the correlation is sufficiently high by checking if model rankings are also correlated well enough -- especially for generators that have a very high, similar performance. Have you looked into such experiments next to the results in the appendix (Figure 6 etc)? The answer might depend on how valuable the small model difference might be, or if preserving the ranking of models is required. The danger is that developers might start to optimize for a potentially noisy metric when comparing only the best models or marginal improvements over the best models. \n* The preprocessing as described in Appendix D.2 might be very suboptimal for some of the ML models from AutoGluon (as they expect to do their own model-specific preprocessing). But this make-everything-continuous preprocessing is needed for many of the generators, correct?  \n* As a final question / side note, a public, easy-to-share leaderboard of the methods might be cool, such as a Hugging Face leaderboard.", "limitations": "", "rating": 10, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "The authors have executed all the above-mentioned contributions with an extremely high quality. The motivation and reasons for the benchmark are novel and original, and well related to prior work. The work seems highly significant, as it improves upon the benchmarking landscape for tabular data generators and may finally deliver actionable insights that allow us to identify good, usable generators for practical applications. The paper is written very clearly, and all information is easily accessible to the reader.", "weaknesses": "There are no notable weaknesses as far as I can tell. Some of my questions might allude to potential weaknesses, but nothing concrete enough to mention here.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Oral)