A Survey on Deep Learning Approaches for Tabular Data Generation: Utility, Alignment, Fidelity, Privacy, Diversity, and Beyond
Authors: Mihaela C. Stoian
Eleonora Giunchiglia
Thomas Lukasiewicz
Venue: Accepted by TMLR ()

Abstract: Generative modelling has become the standard approach for synthesising tabular data. However, different use cases demand synthetic data to comply with different requirements to be useful in practice. In this survey, we review deep generative modelling approaches for tabular data from the perspective of five types of requirements: utility of the synthetic data, alignment of the synthetic data with domain-specific knowledge, statistical fidelity of the synthetic data distribution compared to the real data distribution, privacy-preserving capabilities, and sampling diversity. We group the approaches along two levels of granularity: (i) based on the requirements they address and (ii) according to the underlying model they utilise. Additionally, we summarise the appropriate evaluation methods for each requirement, the relationships among the requirements, and the specific characteristics of each model type. Finally, we discuss future directions for the field, along with opportunities to improve the  current evaluation methods. Overall, this survey can be seen as a user guide to tabular data generation: helping readers navigate available models and evaluation methods to find those best suited to their needs.

Published in Transactions on Machine Learning Research (02/2026)
A Survey on Deep Learning Approaches for Tabular Data Generation: Utility, Alignment, Fidelity, Privacy, Diversity, and Beyond
Mihaela Cätälina Stoian University of Ouford, Imperial College London
wn.stoian@Simeriall.co uk
Elconora Giunchiglia
gejkanchigkaaa@nmeriaaad uk
Imperial College London
Thomas Lukasiewicz
thomas. www../awwaaiiiieeeuueeen...mmmm
Vienna University of Technology, University of Oxford
Reviewed on OpenReview: https:
// openreview. net/ forum? id= RoShSRO067
Abstract
Generative modelling has become the standard approach for synthesising tabular data. How- ever, different use cases demand synthetic data to comply with different requirements to be useful in practice. In this survey, we review doep generative modelling approaches for tab- ular data from the perspective of five types of requirements: utility of the synthelic data, aligmment of the synthetic data with domain-specific knowledge, statistical fidelity of the synthotic data distribution compared to the real data distribution, privacy-preserving capa- bilities, and sampling diversity. We group the approaches along two levels of granularity: (i) based on the requirements they address and (ii) according to the underlying model they utilise. Additionally, we summarise the appropriate evaluation methods for each require- ment, the relationships among the requirements, and the specific characteristies of each model type. Finally, discuss future directions for the field, along with opportunities to improve the current evaluation methods. Overall, this survey can be seen as user guide to tabular data generation: helping readers navigate available models and evaluation methods to find those best suited to their needs.
1 Introduction
In recent years, the synthesis of realistic tabular data has emerged critical research area, driven by the need for privacy-preserving machine learning, robust AT benchmarking, and data augmentation in high- stakes applications such as finance and healthcare. The successful deployment of deep generative modelling led to synthesisers with the ability to improve utility in downstream tasks (c.g., Kim et al. 2023) reduce data scarcity by augmenting existing datasets (e.g., Jia et al. 2024 ), and create new datasets in scenarios where privacy an important concern (c.g., Vero al. 2024 and anonymising data is a challenging task.
Yet, synthesising such data comes with unique challenges that distinguish it from unstructured domains like computer vision natural language. Indeed, differently from images or text, where data is homoge- ncous and presents spatial or sequential corrclations, tabular data is inherently heterogencous, comprising a complex mix of continuous, discrete, and calegorical features with diverse distributionn ions. Further, the re- lations between these features are often non-linear and lack the local structures and patterns leveraged by standard deep learning architoctures such as convolutional neural networks. Hence, synthesisers for tabu- lar data face the complex task of faithfully reconstructing these correlations while also handling inherent irregularities such data imbalance. Moreover, once the data is generated, evaluating its quality proves

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Start: Select
Generator
Scusitive data?
15
dilliiiiciiiialtty?? (> 36 leatures)
No
Fast
Fast
Yoa
Infereuce?
Tie
Inference?" 10k sample))
< 10c somplee)
Types?
Yia
MaIGAN Reeative NN
ILAAA Tusii Tranft B.AN
Gust CLTS
TEGGU
GAN PWTSI GAX
Need constroints?
doalidiimmniionllty? (> ab frstuns))
Fust Inferenee? (<C por samples)
Fust inference?
(<) 10kk samples)
Mixed Typoe?
Mixod Types?
Mixed Typee?
W+
Mixed Types?
Reregy TakeFGrr
GAN BN GANELE
Prtoritive Nlivenity??
Priorition Tilvouity?
Ai
Prioritian Nivendity?
Yea
Pricettbee Divereity?
VAR & CNNN COOALE
Diffisson Sha6
Diffisin C-D:
Diflusion The D-PM
GAN OET BAN TIVAR
DHE Trensh: TorPiN
LIM-
CWEENN
CTTAD-GA
CE TGAA
ISSGAN
Noud constraiate?
C DGM
Figure 1: Simplified roadmap to help select an appropriate tabular data synthesiser based on specific re- quirements, as well as other considerations such as whether the data is high-dimensional and whether the sampling time needs to be low. Note that in this roadmap, we consider fast the models that take less than second to generate 10k samples.
challenging Nacom et al. 2020 Räisä al. 2025 particularly regarding whether statistical inferences can
be faithfully reproduced Montoya Perez et al. 2024 as there is no single metric capable of capturing all the desired requirements.
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These diverse needs and technical challenges have led to not only proliferation of different generative models, but also to an explosion of diverse evaluation metries whose aim is to evaluate whether a model is able to address all the requirements of the given use case. However, the sheer diversity of these metrics has made increasingly difficult to assess and compare different synthesisers in a standardised manner.
This survey analyses models and evaluations methods alike from the point of view of the user, categorising them on the ground of the requirements they address and measure: utility, alignment, fidelity, privacy, and diversity. The analysis thus serves structured resource for both newcomers and experienced practitioners seeking a formal evaluation framework for tabular data synthesis. To this end, we first give overview of the tabular data synthosis problem and its roquirements ($2). Then, we detail each requirement along with its evaluation protocols and metries ($3), but also the relationships among these requirements ($3.6). Next, we survey the existing deep learning generative models for synthesising tabular data ($),, grouping them by their model architecture, but also by the requirements they address, as shown Table | and in Figure 3. In particular, Table [ can be seen as a summary of the surveyed approaches (ordered by their date of publication), providing also an overview of the characteristics for each model, such as their ability to handle high-dimensional and mixed data types, as well as their sample generation times. We lastly review other deep generative models originally developed for other fields (such as natural language processing and computer vision), which can be adapted to tabular data synthesis ($4.6). We conclude with discussion on related surveys and future directions and opportunities for improvement ($5)
Crucially, throughout this survey, we analyse the key requirements that practitioners typically face when synthesising data. Building on this analysis, in Figure [ we present a roadmap designed guide readers in selecting the appropriate synthesiser for their specific use case. This roadmap thus serves simplified visualisation of the surveyed methods, with methods' grouping based on critical considerations such as data sensitivity, hign-dimensionalitt, sampling speed, but also the need for the generated data to adhere to domain constraints. Notably, the decision to enforce domain constraints is positioned as final step. Indeed, in case constraints are needed, the listed methods to guarantce their satisfaction can be simply built on top of a given synthesiser as they are iablle layers able to be integrated inlo any neural network model during training. Conversely, the decision regarding privacy is fundamental and, thus, appears as the first step in the roadmap, specifying whether specialised privacy-proservinn mechanism is required from the start.
2 Synthesising Tabular Data
Tabular Dataset. In the tabular data synthesis field, a tabular dataset D is a collection of N i.id. samples (indexed by i {1....;N) NN such that the i-th sample constitutes the i-th row) drawn from an unknown joint distribution Px over the variables (i.e,, columns) X2,,.. Xx). Thus, for each i {1...., N), the sample x² === = #2,.......... ..kk) is an assignment of values to the variables (X1, X2,...... ... (iy....K),,, i.e., x] E D is the value assigned to variable Xj. for each j (1....,KK K}, where B is the set of permissible values for variable X3. One of the many challenges of this field is given by the fact that the domain of each feature can be very different from one another. Common domains are: binary domains, ie.., DD = {0, 1}. categorical domains, e.g., D = {Red, Yellow, Blue), and numerical domains, iee. D C R. Given dataset D with N > 1, it is always possible to partition its instances in order to obtain a training set used to train a machine learning model, and a test set used to test a machine learning model.
Deep Generative Modelling for Tabular Data.
To formulate the problem of tabular data generation, the literature makes the assumptions that given tabular dataset D, there exists an unknown joint distribution px over the random variables (x,, Xx), where X, E DV, such that D was created by drawing N i.i.d. samples. The goal of standard generative modelling is to learn from D the parameters 0 of a generative model such that the model distribution po approximates px.
While synthesising tabular data is long-standing problem Reiter 2005 in this survey, we focus on methods that use deep generative models, i.e., models based deep neural networks.
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Table 1: Overview of the surveyed methods proposed for syuthesising tabular data. For each work, we report (i) the model type, (ii) whether the model allows for mixed data types (marked with "V" if so, and with "x" otherwise), (iii) the maximum number of features used for evaluation (indicating whether the model can handle high-dimensionallty data), (iv) the model's data generation time relative to the other models. In the last five columns, we indicate with "V" (resp., "x") the requirements that were (resp., were not) addressed, and with the requirements whose resolution depends on the base DGM model upon which the Constraints-enforcing methods are built. Specifically, these requirements are: (v) utility, (vi) background knowledge alignment, (vii) statistical fidelity, (viii) privacy, and (ix) diversity. Regarding the generalion time, the three indicators are assigned based on the time (in seconds) takes to generale 10K samples, as follows: fast for generation time less than 0.5 8, medium for generation time higher than 0.5 but less than and slow, otherwisc. Further, note that "_" indicates that data are not available, and "W" indicales that the method provides guarantees that the domain-specifee constraints are satisfied. Note that the generation time values have been collected from the surveyed papers, aggregated and had thresholds applied to them to assign them to one of the three possible indicators provided, i.e. fast, medium, and slow.
Model
Mixed Max.# Generation
Model
Utility Alignment Fidelity Privacy Diversity
Type
Data Features
Time
modGAN Choi
2017
GAN & AE
1071
fast
/
TGAN
Xu & Veeramachaneni
2018
GAN
V
55
medium
/
x
/
X
TableGAN
Park
2018
GAN
V
medium
1
PATE-GAN
Youn et ul
2019
GAN
/
617
fast
x
x
X
/
ITS-GAN
Clee
GAN AE
CTGAN
Xu ot al 2019
GAN
/
785
fast
/
X
X
VAE
Neural Spline Flows
Durkan al.
2019
Normalising Flows
X
OWGAN
Engelmenn
Lessnann
2021
GAN
OCT-GAN Kinn
2021
GAN
medium
GANBLR Zhang ct al.
2021
GAN & BN
X
CTAB-GAN Zhao
2021
GAN
medium
IT-GAN Lee et al
2021
GAN & AE
slow
GEM
Ierative
DP-MERF
Harder et al.
2021
Kernel-based NN
617 fast
GOGGLE
GNN
CTAB--AN ++ Zhao ml.
2022
GAN
55 mediimn
TsbDDPM
Koteluikov et
2023
Diffusion
slow
STaSy
Kin
2023
Diffusion
slow
CoDi
Lee et. al.
2029
Diffusion
31
medium
GReaT
Borisov
2023
LLM
slow
TabPPGen
Ma et al.
2023
Energy-based model
X
C..TGAN
Hau
GAN BN
FinDif
Sattazov et al.
2023
Diffuston
84
slow
Suh
2023
Diffusion
DP.NTK
Yang es al.
2024
Kernel-based NN
617
fast
TDGGD
es
2024
Diffusion
C-DGM
Stoien al
2021
Constraints-nfferiing
109
fast
TabSSu
Zhaang et. al.
2024
Diflusion & VAE
medium
CuTS
Vera
2024
GAN
TabuLa
Zhao et al.
2025
LLM
slow
DGM+ DRI.
Stoian Clunchiplia,
2025
Constraints-enforrinng
fast
W
Tab TrN
Zhang et al
2025
Trausormer GAN
/
59
X
/
TabPFN
Hollmann
Transfornr
GEM+
Maddock al.
2025
Iuraaive NN
x
123 fast
X
X
Requirements over Synthetic Data. While above we have the goal for standard generative modelling, we know that different use cases can lead additional requirements, which lead different goals for the generative task. In this survey, review the following requirements:
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1. Utility requirement: Synthetic data should yield similar predictive performance to real data when used to train machine learning (ML. models for the same lask, such as classification or regression. For instance, given a healthcare dataset like WIDS Matthys et al. 2021], which contains medical records of patients from the first 24 hours of intensive care, and the target column specifies whether a patient has been diagnosed with diabetes mellitus, training a classifier on synthetic data should yield comparable (or better) performance on the real test set to that obtained by training the classifier on real data of the same size. Hence, given an ML. model m and a predictive performance metric r (e.g,, accuracy), maximising utility entails learning from D the parameters 0 of generative model such that training m on the dataset D' sampled from po leads to the best score according to r.
In addition to predictive performance, utility can be broadly defined as the preservation of valid statistical inferences Raghumathan et al., 2003]. For instance, in differentially private settings, Rosenblatt et al. 2023 quantify this as the likelihood that the empirical conclusions derived from the real data would not change if synthetic data were used instead. In these cases, maximising this statistical utility boils down to maximising this likelihood.
2. Alignment requirement: Synthetic data should aliga with any known (roer-provided) domsin-specific knowledge. The knowledge can be expressed in multiple ways: simply as constraints on the range of values that a single feature can assume, or as more complex constraints capturing relations bet ween the features. Continuing the example above, if the minimmum and the maximum haemoglobin level are two of the features recorded for each patient, then clearly the real data do not contain any records for which the value of the minimunn is higher than the value of the maximum level. This type of constraint easily captured using a linear inequality. Hence, given a set of constraints expressing some background knowledge about the sample space of px, i.e., stating which samples are admissible and which are not, the goal is to learn the parameters i of a generative model such that (i) the model distribution pe approximates px, and (ii) the sample space of pe is compliant with the constraints.
3. Fidelity requirement. Synthetic data should preserve the statistical properties of the real data. Continuing with our example, if we are maximising fidelity on the WIDS dataset, then the distribution of the syuthetic values of the minimum haemoglobin level feature should resemble the real distribution of the same feature. Hence, in this case, the goal is to learn parameters 0 such that the marginals of po are similar as possible to the corresponding marginals of px, and the joint distribution po should closely follow Px.
4. Privacy requirement. Syuthetic data should present minimal risk of disclosing sensitive attributes and of re-identifying individuals from the real data. Continuing the earlier example, the WIDS dataset contains sensitive features such as the patient's age, whether the patient had an elective surgery, and whether the patient received leukemia diagnosis. If a rare combination of values for these features is retained in the synthetic data, then patient might be identified, hence failing to meet privacy requirements. Hence, in this case, the goal is to learn the parameters 0 such that it is impossible to sample a data point from po that would allow for the re-identification (or for disclosing sensitive attributes) of a real data point.
5. Diversity requirement. Synthetic data should cover the full variability of the real data distribution. While closely related to fidelity, diversity focuses on a different aspect of the data distribution. Specifically, diversity ensures that the model does not omit regions of the output sample space, which is what would happen in the case of a mode collapse, for example. Continuing the earlier example, it is likely that the WiDS dataset contains under-represented patient groups, such as young adults with specific co-morbidities or rare physiological responses, e.g., captured as extreme but valid laboratory test result values. In such cases, failing to meet the diversity requirement might only produce "average" patient profiles. Thus, the goal is to learn parameters f such that the support of po fully covers the support of px, which would allow for rare feature values or combinations of values to be synthesised (with appropriate probability).
TTo further clarify our categorisation, we acknowledge the possible terminology overlap with previous papers. For example, Xu al. 2019 mention that the discriminator of CTGAN trained such that the synthetic data aligns with the real data. However, this case, the term align used informally and refers to the process of matching the real data distribution, which falls under the fidelity requirement our survey. The formal definition of alignment has been introduced in Stolan et al. 2024. and is reproduced here to convey alignment with the given background knowledge.
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Table 2: Overview of the evaluation metrics typically used for the five syuthetic tabular data requirements.
The formula and terminology definitions for each metric are provided in Appendix A
Requirement
Evaluation Metric
Accuracy
F1-score
Utility
Root mean square error (RMSE)
Explained variance
Epistemic parity
Constraint violation rate (CVR)
Alignment
Constraint violation coverage (CVC)
Sample-wise constraint violation coverage (sCVC)
Wasserstein distance
Kolmogorov-S Soiinooov--nonvvvoooooo test statistic
Feature-wise wise
divergence
Total variation distance
RMSE differences mutual information MAE differences in mutual information Correlation difference
Pair-wise
Fidelity
Likelihood fitness score
a-Preeiisoo
Joint
Density
Clipped density
AUCROC (for membership attacks)
Precision (for attribute disclosure attacks)
Recall/Sensitivity (for attribute disclosure attacks)
Privacy
Distance the closest record (DCR)
Nearest neighbour distance ratio (NNDR)
k-anonymity
8-Recall
Coverage
Diversity
Clipped coverage
3 Requirements and Evaluation Metrics
To systernatically evaluate the quality of synthetic tabular data and guide the selection of appropriate synthesisers, in this section, we detail each of the five requirements, along with the specific evaluation protocols and metrics used to quantify them, and discuss their significance in real-world applications.
For each of the five requirements above, Table 2 lists the metrics that commonly used to evaluate the generated data. Further, in Appendix A. we provide the formula for cach of these metrics, along with the terminology definitions.
3.1 Utility
Determining whether synthetic data replace real training data in downstream tasks has been the most common evaluation approach (e.g., [Choi et al.) 2017 Park et al. 2018 Kotelnikov et al. 2023 Borisov al, The main reason for this is that synthetic data are often generated to augment or create datasets for real-world applications, including high-stakes fields like finance and healthcare. In these scenarios, generaling synthetic samples for rare events, e.g., fraudulent transactions and specific medical diagnoses Matthys et al. 2021,, can help with class balancing and ultimately improve the quality of the predictions downstream tasks. Therefore, utility still remains a key requirement for synthetic data and benchmark for comparing synthesisers.
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Evaluation Protocol and Metrics. The most common protocol used to evaluate the utility of generative models is the Train on Synthetic, Test on Real (TSTR) Protocol (see, e.g., Esteban et al. 2017): ) The procedure is to train a suite of ML models (e.g,, a support vector machine, XGBoost) on the synthetic data, and then test their performance on a real test set, reporting the performance using different metrics on the ground of the lask defined by the dataset of interest: for classification (resp., regression) datasets, slandard metrics include accuracy and F1 score (resp., root mean square error and explained variance).
Beyond predictive performance (TSTR), foundational work on classical statistical, non-deep learning meth- ods for generating fully synthetic data in [Rahumathan et al. 2003 aimed to preserve the users' ability to obtain valid statistical inferences without compromising the confidentiality of survey respondents. Further, in the specific case of differentially private settings, recent work by Rosenblatt et al. 2023 similarly argues that syuthetic data must also support valid inference, ensuring that statistical conclusions derived from real data are preserved. To mcasure this, they introduce a metric called epistemic parity, which evaluates whether empirical conclusions of peer-roviewed papers on real, publicly available data can be reproduced on synthetic datasets. To this end, in the context of synthesising data intended for scientific discovery, MMnnoyy Perez et al. 2024 emphasise that evaluating the validity and power of statistical tests is essential.
3.2 Alignment
Brought to the attention of the rescarch community more recently Chen et al., 2019 than the other re- quirements, background knowledge alignment is an important condition for synthetic data when evaluating its realism. This requirement is important in practice, as many real-world applications have domain-specific knowledge that the synthetic data must satisfy. For example, synthetic patient data in healthcare must adhere to physiological constraints, ensuring recorded minimum value for an indicator (like blood pressure or haemoglobin level) is not higher than the maximum value recorded. Similarly, in finance, it is important for generated market data to comply with known economic constraints. In resource management, synthetic inventory and demand data must not violate logistical constraints, such as production capacity limits or non-negative stock levels.
Evaluation Protocol and Metrics. In Stoian et al. 2024], , three metrics have been proposed to evaluate alignment: (i) the Constraint Violation Rate (CVR), which computes the percentage of samples that do not satisfy at least one of the constraints in the available set of constraints, (ii) Constraint Violation Coverage (CVC), computing the percentage of constraints that have been violated at least once by the sample set, and (iii) the sample-wise Constraint Violation Coverage (sCVC) which determines the average percentage of samples violating each of the constraints. Out of these three metrics, CVR has also been used in Jia et al.
2024 albeit called fcasibility rate there.
3.3 Fidelity
While statistical fidelity is not a good predictor of dlwnnstream task performance Hansen et al. 2023 it can provide useful observations on how the synthetic data compares to the real data. Fidelity is indeed one of the requirements often evaluated in early works on synthesising tabular data and it is crucial for applications such as cconomic modelling and census data release. In these arcas, preserving the statistical properties of the real data distribution, like demographics, allows for accurate downstream sociological and economic analyses. Similarly, generating data that captures the statistical complexity of real-world data is valuable in other domains, such as the robust testing of data processing software.
Evaluation Protocol and Metrics. Being the longest-standing requirements, a. large number of methods were developed to evaluate the statistical fidelity of synthetic data w.r.t. real data These can be categorised into (i) feature-wise, (ii) pair-wise, and (iii) joint evaluations.
Feature-wise evaluation: compares synthetic and real data feature by feature, using different metrics basod on feature type. For continuous fcatures, Wasscrstein distance and the Kolmogorov-
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Smirnov test statistic are common, while Jensen-Shannon divergence total variation distance are common metries for discrete features. The difference in treatment is supported empirically in [Zhao] et al. 2021, , which found that Jensen-Shannon divergence is unstable for measuring the statistical similarity between continuous features' distributions, especially with no overlap between synthetic and real data.
2. Pair-wise evaluation: investigates how well relationships between pairs of features are preserved in the synthetic w.r.t. the real data. Common metrics include: (i) RMSE (and MAE) differences in mutual information between pairs of features, and (ii) correlation difference, using Pearson's coefficient for contimuous pairs, Theil's uncertainty coefficient for discrete pairs, and the correlation ratio between discrele-continuuus pairs of features.
3. Joint evaluation: compares the joint distribution of the synthetic samples against the real samples' distribution. It is more difficult to determine how similar are two (potentially high-dimensional) joint distributions. Thus, such an analysis is often conducted in a controlled environment, e.g. on simulated data, rather than real-world data. Relevant evaluation methods include measuring:
(i) the likelihood fitness score, separately for real and synthetic data (as in Xu et al.) 2019 ) (ii) a-precision Alaa et al.) 2022]. which is a variant of precision representing the fraction of synthetic samples that resemble the most typical fraction a of real samples, (iii) density (defined in Nacem let a.l.
2020 ), which improves upon the standard precision metric by counting the nunber of real
manifolds each synthetic sample falls within, and (iv) clipped density, which has been proposed by (aaly et al. 2025 as an improvement on the density metric in terms of robustness, clipping the radius of the nearest-noighhour manifolds used to measure the density to the median of the distances to the k-th nearest neighbour.
3.4 Privacy
Synthetic data are particularly valuable in privacy-sensitive domains. Thus, there has been growing focus generating data without revealing sensitive information that could identify entities from the original dataset. For example, sharing synthetic patient records for medical research allows for collaboration without risking the re-identification of individuals or the disclosure of sensitive health information. Similarly, privacy is an important requirement in education analytics, where synthetic educational data allows for studying student performance trends without exposing individual student identities or sensitive background information. Fi- nance is another key domain where privacy is concern and synthesising transaction or credit data to be released for academic commercial rescarch must be done in way that protects customer confidentiality.
Evaluation Protocol and Metrics. Privacy is typically evaluated by assessing the risk of attacks suc- ceeding in targeting sensitive information. The most common attacks are: (i) membership inference attacks, which use ML classifiers or black-box attacks (e.g., see Chen et al. 2020) ) to determine whether an entity was part of the set used to train a model, (ii) attribute disclosure attacks, which try to gain access to sensitive attributes of an entity from the real dataset, and (iii) re-identiffcation attacks, which try to map a synthetic data point back to the original dataset. To measure the risk of the attacks being successful, for (i), AUCROC is often reported for the trained attack models (lypically one for each class of a feature of interest). However, this metric can be misleading, as it might suggest that a model is secure even the privacy of few users has been confidently breached or, conversely, imply that an attack successful basod on unreliable scores. To this end, Carlini et al. 2022) argue that membership inference attacks should be evaluated using the true-positive rate (TPR) at low false-positive rates (FPR), which is capable of detecting such high-confidence attacks that aggregated metrics, such as AUCROC, might overlook. For (ii), precision and sensitivity (i.c., recall) are mcasured while varying the number of attributes known to the attacker, and, for (iii), common metrics include: the distance to the closest record (DCR) Zhao el. al.) 2021 (computed as the minimum L2 distance from a synthetic data point to each real data point), the nearest neighbour distance ratio (computed as the ratio between the distances to the closest and sccond-closest real neighbours for synthetic record), but also k-anonymisation, delta presence, and the identifiability score, as seen in Jia
et al. 2024
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Finally, methods using differential privacy Dwork 2006 introduce noise during training to reduce retention of original data features. Privacy is then evaluated using different privacy budget values, which determine the amount of added noise and balance utility and privacy (e.g., see Park et al. 2018 ).
3.5 Diversity
While fidelity ensures that generated samples resemble the real ones, diversity ensures that the synthetic data cover the full variability of the real data distribution [Neem et al.) 2020 This plays an important role in avoiding mode collapse, where a synthesiser produces samples that fit well within the data distribution but which are repetitive, failing to represent rare feature combinations or outliers which are present in the real data. This is of particular importance in healthcare as described carlier, but also in domains such as finance, e-g.; for detecting fraud patterns.
Evaluation Protocol and Metrics. Typically, diversity is evaluated by determining the proportion of the real data manifold that is represented by the generated data. There are multiple ways to compute this, with the most common metrics being: (i) 8-recall Alaa et al. 2022 which is a variant of recall evaluating whether the synthetic data covers the variability of the real data (e.g., as used in Liu et al. 2022) ; (ii) coverage (defined in Naeem et al. 2020) and used in Kim el al. 2023 Kotelnikov et al. 2023 which improves upon the standard recall metric by building nearest neighbour manifolds around the real samplos, instead of around the synthetic samples, to ultimately mcasure the proportion of real samples whose neighbourhoods contain at least one synthetic sample, and (iii) clipped coverage, which has been proposed by Salvy et al.) 2025 as an improvement on the coverage metric in terms of robustness (e.g.. unlike the standard metric which only checks for the presence of synthetic samples within the real manifolds, clipped coverage counts them and bounds their contributions to effectively reflect the real data distribution rather than just its support).
3.6 Relationships among the Requirements
As emphasised by Naeem et al. 2020 assessing a generative model an inherently difficult task, as no single metric can capture all the desired propertics of synthetic data. And, while the requirements described in Sections 3.1 3.5 are presented individually, they are not orthogonal. In fact, these requirements relation- ships vary from mutual reinforcement to mutual tension, possibly leading to tradeoffs. Thus, forming an understanding of these relationships is crucial for practitioners to select the appropriate synthesiser for their specific use case.
Fidelity and Utility. Intuitively, higher statistical fidelity, where the distribution of the synthetic data Po closely approximates the distribution of the real data px, often yields higher utility. However, this is not always the case, as a high statistical fidelity does not guarantee optimal utility in downstream tasks and vice-versa. Indeed, shown by Hansen et al. 2023 fidelity alone is insufficient. for assessing the synthetic data's utility, and should not be used as an indicator for it.
Alignment and Fidelity. The relationship between these two requirements can be seen as hierarchical. A model with "perfect" " fidelity would implicitly satisfy all background knowledge constraints present in the real data, assuming such data do not contain any errors. However, high alignment does not necessarily imply high fidelity. In spite of this, alignment plays a vital role for any model that to be deployed in domains where constraints must be guaranteed Stoian et al. 2024. whereas fidelity often remains an approximation.
Furthermore, it is still possible to have real data that contains erroncous values (e.g., swapped minimum and maximum values due to human error). In such cases, the constraints can be used to validate and correct the data before synthesis. Indeed, if these errors are not addressed, model that strictly satisfies the alignment requirement may inevitably deviate from statistical fidelity measured in this case against the corrupted real data.
The tension between privacy and utility is perhaps the most critical trade-off in tabular data synthesising. In particular, any method that claims to
The Privacy Trade-off (Privacy, Fidelity, and Utility).
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GAN-based model
VAE-based model
Diffusion- Diffusion-based model
Forward Diffusion
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Discriminator
Generator
Encoder
Decoder
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Figure 2: Visualisation of common model types used for synthesising tabular data. Here, æ, 2, and denote real sample, noise sample, and synthetic sample, respectively; H' is sample modified by based models; is the sample at step i of forward diffusion (for i in (1....,7) T), where T is the maximum number of diffusion steps); and ž; is the sample at step i of reverse diffusion.
be preserving privacy must balance privacy and utility jointly rather than separately Montoya Perez et al.) 2024. To satisfy differential privacy, for example, noise must be added during sample generation. And, more such noise is added (i.e., to better protect the data subjects), statistical fidelity decreases, which often leads to lower downstream performance (i.e., utility). It is thus important for synthesising methods to determine the acceptable extent of utility to be sacrificed in order to achieve robust privacy guaranteos.
Diversity and Fidelity. Intuitively, fidelity and diversity are associated with precision and recall, re- spectively (aajadi el al. 2018 Naeein et al. 2020 Models suffering from mode collapse may still produce high-fidelity samples (i.e., high-precision), but fail to cover the full variability of the real data distribution (i.e., low diversity or low recall). Conversely, maximising diversity may result in generating outliers or noisy samples, which often leads to lower fidelity. Thus, these two metrics are seen as complementary trade-offs. as maximising one without the other leads to suboptimal synthetic data. Further, an effort to disentangling fidclity from diversity, different metrics have boen proposed to mcasure cach of the two requirements, which were often improved precision and recall variants first. presented in KKykaääniemi
al.) 2019 and subsequently in Naeem et al. 22200] ; Alaa et al. 2022 ). Nevertheless, the recent position paper by Räisä ct al. 2025 argues that current metrics for measuring fidelity and diversity are flawed and advocates for metrics with meaningful absolute values, rather than just relative comparisons, to truly determine if a model is useful in practice.
4 Methods
Having established The key requirements for synthetic tabular data, we now survey the deep generative models designed to meet them. To provide a clear structural overview, we categorise these approaches basod on their underlying generative paradigm: generative adversarial networks (GANs), diffusion models, transformers and large language models (LLMs), variational autoencoders (VAEs), constraiins--nffrrinng methods, along with other deep learning methods (e.g., approaches stemming from other domains but which
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have been adapted to tabular data synthesis). Finally, we also discuss briefty non-deep learning alternatives.
4.1 Generative Adversarial Network-based Methods
4.1.1 GAN-based models
Many of the works surveyed here are based on the original Generative Adversarial Network (GAN) Good- Tellow et al.] 2014], which relies on two neural networks: (i) a generator, which given a noise vector returns a synthetic datapoint and hence learns the real data distribution, and (ii) a discriminator, which given a data point (cither real or synthetic) classifies it either real synthetic and hence Iearns to distinguish between synthetic and real data. The GAN jointly trains these two models in an adversarial framework, where the generator's s objective is to produce samples that confuse the discriminator. See the first schema from the left in Figure 2 for a simple abstraction of GAN-based models.
CWGAN: Building on the seminal Wasserstein GAN (WGAN) Arjovsky et al.
2017 which used the
Wasserstein distance as a loss function for a GAN model, Engelmann Lessmann 2022 proposed CWGAN as an oversampling framework for class balancing. CWGAN generates synthetic samples for underrepre- sented classes, augmenting the training set. Results indicate that oversampling is beneficial primarily for strongly non-linear datasets. OCT-GAN: proposed by Kim et al. 2021 incorporates neural ordinary dif- ferential equations (ncural ODEs) in their GAN through the introduction of a new layer that allows for the extraction of a sequence of hidden veclor representations given an input sample, i.e., the hidden evolution trajectory of the sample. The trajectory is used to help the discriminator decide whether a sample is real or synthetic. While improving utility, the usage of ODEs makes OCT-GAN slower than most GAN-basod models. TGAN Xu & Veeramachaneni 2018 is an carly GAN-based model that proposes using long short- term memory networks with an attetion mechanism to synthesise data sequentially, feature by feature, in order to model tabular data of mixed types. Comparing with conventional statistical models and showing better fidelity performance, TGAN contributed to the popularity of the GAN-based approaches for tabular data.
CTGAN: focused on better modelling the types of the variables in an effort to increase fidelity. Indeed, the authors propose a new preprocessing method, which chumn-type-specifff and models discrete features in the continuous space via Cumbel--Sfftax transformations, while it employs mode-specific normalisation via variational Gaussian mixture model applied for each continuous features. Thanks to these transformations.
CTGAN is able to avoid mode collapse, which often burdens other GAN-based models, like medGAN Choi and TableGAN Park et al.) 2018 CTAB-GAN: Building upon CTGAN, CTAB-GAN Zhao
lt al.
2017
et al. conditional vector to handle mixed-type fcatures and multi-modal continuous variables, extending support beyond discrete and continuous features. Further, it supports mixed-type features: which are features that might have highly-recurring discrete values, but also continuous values across the data points (e.g., feature Credit Card Transaction USD might often have value 0, but it can also exceed 500). The benefit of providing support for mixed-type features is reflected in the fidelity performance, with CTAB-GAN outperforming CTGAN. CTAB-GAN+ Zhhoo et al. 2022 is an extension of CTAB-GAN, which addresses privacy concerns by training a discriminator using differential private-SGD Abadi et al. 2016. Importantly, CTAB-GAN+ demonstrates high fidelity performance.
2021 enhances statistical fidelity by addressing data imbalance and long-tail issues. It introduces a
Another model that marked an important milestone for deep generative modelling of tabular data is TableGAN Park et al. 2018), which, unlike medGAN, can model continuous features. While it is based on standard GAN model, consisting of a generator and a discriminator, TableGAN has an additional component: a classifier that predicts the value of the target feature for synthetic samples using semantic integrity constraints learned from the real data. As excmplified in the original paper, sample with values of 60 and 1 for features Cholesterol and Diabeles, respectively, does not align with the background knowledge, as the cholesterol level is too low for the target feature to indicate a diabetes diagnosis. Focusing on ensuring privacy, the authors argue for the use of synthesiser models, which do not learn bijective relationships between real and fake data, making them less vulnerable re-identification attacks, unlike prior perturbation or anonymisation methods. Indeed, TableGAN shows that it can synthesise tabular data with a low risk of re-
TableGAN:
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identification attacks, membership inference attacks and attribute disclosure attacks to succeed. PATE-GAN: Another model that is based on a GAN architecture, but alters it for preserving privacy, is PATE-GAN Yoon et al. 2019. Rather than using the standard GAN discriminator, PATE-GAN relies on a modified Private Aggregation of Teacher Ensemble (PATE) Papernot et al., 2017 mechanism to ensure that the discriminator is differentially private. More specifically, a number of leacher-discriminnttos are created and trained to improve their loss w.r.t. the generator; which adjusts its loss according to the single student-discriminator in the mechanism. In turn, the student-discriminator adjusts its loss according to the leacher-discriminator and allows for backpropagation to the generator, closing the loop. Critically to the privacy requirement, specialising each of the vacher-discrimnntooss on small partitions of the training set ensures that the effect of individual samples is small and, thus, higher differential privacy.
CuTS: Vero et al. 2024 proposed CuTS as a customisable framework, which can adapt to user-defined specifications, such as background knowledge constraints, but also to differentially private training. In the private sctting, CuTS builds on the DP itcrative framework from McKenna et al. 2022.. but uses its own GAN-based generator, which is equipped with a mechanism that matches the generator's output distribution to the real data distribution by comparing marginals. Additionally, CuTS can incorporate background knowledge in the form of propositional logical constraints that cach data point must satisfy via a new loss term. Further, rejection sampling is used to ensure that the model's outputs satisfy the constraints. Although the framework works only with discrete features, it takes a step towards synthesisers for tabular data that account for multiple requirements, including alignment and privacy.
4.1.2 GAN and BN-based models
GANBLR: [Zhang et al. 2021 construct the generator and discriminator as Bayesian net works (BNs), which are able to encode known feature interactions. The background knowledge inclusion leads to better utility than standard GANs, C Similarly to GANBLR, C*-TGAN [aan et al.) 2023 uses Bayesian net- works to capture background knowledge. However, while GANBLR models only discrete features, C3NTNAN can handle both discrete and continuous features by following the CTGAN Xu et al., 2019 approach. To incorporate explicit attribute correlations and property constraints from background knowledge, it repre- sents constraints as control vectors (similar to the conditional vectors in CTGAN) and uses them to guide training, ensuring better alignment.
4.1.3 GAN and AE-based models
ITS-GAN: proposed for tabular data augmentation ITS-GAN Chen et al. 2019 is an early method advo- cating for the use of background knowledge. The knowledge it can express is of two types: (i) rules stating that the value of one feature uniquely determines the value of another (e.g., the feature Position determines the feature Salary), and (ii) rules stating that a specific value for a set of features determines the specific value for another (e.g., if Position = "CEO" then Salary = "2M"). To encode the first types of rules, they train on the real data an autoencoder (AE) for each rule to output the value of the dependent features given the values of the independent ones. Then, at training time, the GAN generator is trained to minimisc the difference between its output and one of the AEs, while also being penalised if it violates any rule of the second type. Additionally, the discriminator receives as input the difference between the AE's outputs and the synthetic samples, thus being able to use this information to assess the sample.
medGAN: Proposed by Choi et al. 2017 for synthesising healthcare datasets, medGAN is one of the pio- neering models for synthesising tabular data using deep generative models. medGAN generates distributed representations of health records using the generator of GAN-based model, then decodes these represen- tations using an autoencoder pretrained discriminator component of the GAN, which is trained to distinguish the synthetic from the real data. In terms of privacy, medGAN showed low attribute disclosure risks, except when an attacker focused on a small number of data points. IT-GAN: Similar to OCT-GAN but designed to enhance privacy robust- ness, IT-GAN Lee et al., 2021 employs a generator based on neural ODEs to balance utility and privacy protection. Instead of directly synthesising samples in the input space, the generator produces hidden rep- resentations, as seen also in medGAN. Notably, ensures that the hidden representation space matches the input dimensionality, enabling the application of ODEs.
the real data, and passes the decoded representations to the
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4.1.4 GAN- and Transformer-basee models
TabTransGAN Zhang et al. 2025 achieves a performance comparable to GReaT Borisov et al. 2023 by combining the strengths of Transformer [Vaswani et al. 2017 and GAN-based models, which allows it to model both contextual and structural relationships across all features. Specifically, TabTransGAN adopts a GAN architecture in which the generator is based on CTGAN, while the discriminator replaces the standard design with Transformer archilecture. This enables it to better capture both feature-wis distributions and dependencies between the features, leading to more accurate discrimination between synthetic and real data.
4.2 Diffusion-baseed Methods
4.2.1 Diffusion-based models
TabDDPM: Motivated by the their success in computer vision, Kotelnikov et al. 2023 introduced TabDDPM: diffusion-based model for synthesising tabular data. Popular for its high utility results, TabDDPM is able to model both discrete and continuous features, but separately, by using multinomial Hoogeboom et al. 2021 and Gaussian diffusion models SSoh-Diicsttein et al. 2015]. respectively. For a simple abstraction on how a diffusion model can be used to generate data, see the central schema in Figure 2 STaSy: Proposed by Kim et al.] 2023]. STaSy is based on a score-based generative model (SGM), which was shown to be a competitive alternative to baatsdd models in [Ho et al.) 2020 Contrarily to TabDDPM, StaSy estimates the score function (gradient of log-probability) instcad of explicitly modelling the forward and reverse Markov processes. As the loss is difficult to train, STaSy uses self-paced learning strategy, which starts with a subset of training data data-yiekding stable, low Evaluated on 15 real-world datasets against 7 baselines (mostly GAN-based models), ST&Sy achieves high utility. Due to the forward and backward passes, both StaSy and TabDDPM suffer from slow sampling times. Moreover; the base SGM model is known to be unstable in high-dimensional settings. CoDi: Motivated by the difficulty of modelling discrete features, [ee et al. 2023 proposed CoDi, a framework comprising co-evolving diffusion models that separately handle continuous and discrete features as in TabDDPM Kotelnikov et al., 2023. with the difference that the two models condition on each other during training. At each training step, the discrete (resp., continuous) diffusion model takes the perturbed sample from the continuous (resp., discrete) one as input, and both models are conditioned on both samples from the previous step during the denoising process. Slower than most GAN-based models (exchuding OCT-GAN), CoDi is faster than STaSy and TabDDPM, while also obtaining higher utility on mixed types datasets.
gradually expands to the full dataset.
The first framework encoding background knowledge about feature relations into diffusion- based models is TDGGD TTa et al. 2024 The relations can express lower and upper bounds over single fratures or their sum. Rather than explicitly modelling the relations, TDGGD models whether the features are part of such relations or not, which only gives an indication of hidden relations between the columns to the model. FinDifl: Motivated by the need to preserve the statistical properties of real data of mixed types in real-world financial contexts, [Sattarov et al. 2023 proposes FinDiff, which is capable of generating mixed-type tabular financial data using- a diffusson model to capture high-dimensional dependencies. Unlike another popular diffusion model, TabDDPM Kotelnikov et al. 2023). which uses one-hot encoding for categorical features, FinDiff employs embedding encoding for better handling of mixed data types. This leads higher fidelity performance compared to the baselines, indicating that FinDiff effectively captures both feature-wise and joint distributions of the data.
TDGGD:
4.2.2 Diffusion and AE-based models
AutoDiff: Proposed in Suh et al. 2023 AutoDiff is diffusion-basee model designed to preserve statistical fidelity by modelling the joint distribution via an autocncoder, rather than modelling the distributions of individual feal separately, as seen in GAN- and diflusion-based models like CTGAN and TabDDPM. More precisely, AutoDiff (i) uses the autoencoder to learn the distribution of the features (which can be of mixed types) in a continuous space, and then (ii) passes these continuous representations to the diffusion model, which generates latent representations that are then decoded back into representations in the original feature space. Moreover, like CTAB-GAN, it introduces approach to handle mixed-type features by
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adding new feature to the autoencoder that encodes the frequency of recurring values in mixed-type feature.
4.2.3
Diffusion and VAE-based models
TabSyn: Introduced by Zhang et al. 2024]. TabSyn trains a score-based diffusion model, like STaSy, but in a joint VAF-learned space of numerical and categorical features. Notably, TabSyn significantly reduces the runtime of diffusion-based models while outperforming basclines w.r.t. fidelity and utility.
4.3 Transformer and Large Language Model-based Methods
GReaT Borisov et al. 2023 represents an answer to the abundance of works that convert tabular data into numerical representations thus losing the contextual connections between the features, which very often carry semantic meaning. Indeod, GReaT performs the following steps (also illustrated in Figure 2 first, the labular data undergoes a textual encoding process, converting it into text. Next, a feature order permutation step applied. The resulting sentences are then used to fine-tune the large language models (LLMs) Vaswani et al. 2017 At sampling time, either single feature are given input to the LLM, which then completes them (note that this allows for arbitrary conditioning). Using this approach, GRea'T outperforms most of the baselines w.r.t. utility, but its data sampling time is notably high. To address this problem, TabuLa ZZhao et al.) 2025 introduces a method to reduce the length of the gencrated token soquences. Unlike GReaT, which relics on large language models pre-trained on natural language processing lasks, TabuLa starts with a randomly initialised model and iteratively fine- tunes it on tabular data synthesis tasks. Another key distinction is that TabuLa does not use GReaT's feature permutation mechanism. Instead, it targets scenarios where arbitrary feature conditioning is not needed and assumes that feature values appear in consistent order across all data points. To this end, the authors tokenise the dataset leature-wise, ensuring that each generated token can be mapped to a specific feature based on its absolute position in the row. Specifically, for each feature, they determine the longest token sequence across the dataset and pad all sequences (corresponding to that feature) to this length during training, Using this approach, TabuLa manages to significantly reduce the training time compared to GReaT. However, its sample generation time is still considcrably higher than GAN-basod models such as CTGAN or TableGAN.
arbitrary feature-value pairs
4.3.1 Tabular Foundational Models
TabPFN Bringing shift in tabular data synthesis, away from training synthesisers each new dataset, the tabular prior-data fitted network (TabPFN) Hollmann et al. 2025 leverages in-context learning Brown et al. 2020 mechanism of transformer-based methods and is pre-trained on a large collection of synthetic datasets rather on than large collections of publicly available datasets. In this way, TabPFN avoids issues such as privacy breaches, copyright infringements, and cross-onttamnattnng the training data with test data. To generate synthetic datasets, uses structural causal models, which are able to represent causal relationships in the data. via directed acyclic graph. Although primarily a predictive model building its preliminary version from Hollmann et al. 2023, it is important to note that TabPFN can also generate tabular data by approximating the joint distribution of features and targets, and is able to outperform the classical methods, such as tree-based baselines, on small- or even medium-sized datasets of up to 10K samples. Given its transformer-based architecture, sampling time during inference is high, but the model intrinsically does not require training, as it can adapt and do inference on unseen real-world datasets.
4.4
Variational Autoencoder-based Methods
4.4.1
VAE-based models
TVAE Xu et al. 2019, proposed along with CTGAN, was designed to check whether CTGAN's generator's
lack of access to the real data during training makes weaker compared to models that do use these data
for training their generator, such as models based on Variational Autoencoders (VAEs) Kingma & Welling 2014 Indeed, TVAE's architecture showed an improvement over CTGAN in terms of fidelity. However, like
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the authors also considered the impact of their proposed models w...t. privacy and noted that TVAE's access to the training data might make it unsuitable in rownstream tasks where sensitive data are present.
4.4.2 VAE and GNN-based models
GOGGLE: Liu et al. 2022 is a different approach which integrates knowledge about pairwise feature dependencies by encoding them in a graph where each feature is a node and an edge exists if a relation bet ween the two features is known. New relations can be learnt using a message passing mechanism from graph neural networks (GNNs), which is jointly trained with a VAE-based architecture, where ouly relationships prioritised by the learned graph influence feature generation. Due to its relational learning graph- based component, it might be difficult to scale GOGGLE to datasets of higher dimensionality.
4.5
Constraints-enforcin Methods
C-DGM: The first method to constrain deep generative models and guarantee the constraints satisfaction proposed in Stoian et al. 2024]. The constraints can capture any set of linear inequalities over the feature space. Differently from the methods surveyed above, this approach relies on a layer to be added right before the sample output layer, which restricts the output space of the model to coincide with the space defined by the constraints, The layer can be added on top of any deep generative model (DGM), and the resulting models are called C-DGMs. For a visual representation on how the layer-based methods can be added on GAN model, see the right-most schema in Figure 2 As the layer is differentiable and acyelic, it can be added both at inference and training time, whilc also improving the utility of the model. DGM-DRL: The above layer was further extended in SSoiaan & Giunchiglia, 2025 in order to capture constraints expressive as disjunctions over linear inequalities (which allow for expressing relations like "if the sum of two features is greater than 10 then the difference of other two features should be lower than 5"), thus modelling non-convex and even disconnected output spaces. The new layer is called Disjunctive Refinement Layer (DRL.), and a DGM constructed using DRT. is called DGM+DRL. Just as C-DGM, DGM+DRT, is able guarantee alignment with the background knowledge, while also improving utility across all considered basclines.
4.6 Other Deep Learning Methods
Normalising flows-based models. Neural Spline Flows: Rather than using the common transforma- tions found in normalising flows, Durkan et al. 2019 proposed using a fully-diiferentiable module based on monotomic rational-quadratic piecewise functions. This adaptation, combined with the inherent properties of normalising flows, which model the data as the output of an invertible differentiable transformation of a noisy sample drawn from a known distribution, can help synthesise high-fidelity tabular data. The authors note that such a result is conditional on having enough training data compared to the datasets dimensionality.
-bacd models. TabPFGen Ma et al. 2023 is a generative model that uses pretrained network energy-based model for data augmentation and class balancing. Although its capabilities are limited to low-dinensional inputs (it was tested on datasets with maximum 10 features), TabPFGen demonstrates good utility performance in the data augmentation task by simply using a pretrained model compared to specialised GAN-, VAE,, and diffusion- models.
NN models. GEM: Addressing the computational bottleneck of differ- entially private query release methods such as MWEM Hardt al., 2012). Liu al. 2021 propose new generative networks with the exponential mechanism (GEM), which can be incrementally updated without retraining from scratch. The novelty of this approach is its capability to represent the data distribution using set of generative models parametrised by neural networks. Unlike the prior methods, this approach avoids the issues which arise from maintaining a joint distribution over the data domain as the number of features increases, all while being able to generate scalability than the prior methods from the literature, it cannot scale to the real-world high dimensionality demands and also suffers from lower fidelity compared the more recent methods, such as AIM McKennal et al. 2022 Conversely, ATM offers high fidelity but fails to scale to high dimensions due to the memory
Iterative privacy-preserving
datasets. GEM+; While GEM offers better
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constraints of graphical models. To tackle this issue, GEM+ Maddock et al. 2025 proposes novel model which integrates the adaptive selection strategy of ATM with GEM's scalable generative networks, while also bringing algorithmic improvements specific to high-dimensional data.
Kernel-based NN Models. DP-MERF: Part of the line of frameworks that develop differentially private algorithms for training deep generative models is the private mean embeddings with random features (DP- MERF) method proposed by Harder et al. 2021. Specifically, DP-MERF uses random Fourier features to approximate the kernel, which in turn allows for releasing differentially private mean embedding of the real data. Given this differentially private embedding, the objective of the model's generator does not have direct access to the data and can then be freely optimised. DP-NTK: Building on DP-MERF, Yang et al. 2024 proposes a model which utilises the features of an empirical neural tangent kernel rather than the random Fourier features used by DP-MERF. This modification enables the model to better capture complex, non-linear relationships in tabular data, improving the balance between privacy and utility over the original DP-MERF, without relying on any public tabular datasets.
Models adapted from other domains to tabular data synthesis. In (3.1 3.5 and earlier in this section, we compared deep generative models originally proposed for tabular data synthesis. Here, we discuss seminal models first developed in other fields and later adapted for tabular data. WGAN: Originally designed for computer vision tasks, WGAN AArovssy et al.] 2017 was introduced in a paper that analyses ways to measure the distance between the real and model distributions, arguing that weaker loss functions induce weaker model topologies, thus weak models for the real distribution. The authors compare the Wasserstein distance with traditional probability distance measures, including Kullback-Leiun Shannon divergence, and total variation distance, showing that the Wasserstein distance has properties that would be better suited for learning distributions in low dimensional manifolds. They thus propose GAN models that use the Wasserstein distance as loss function. WGAN-GP: A popular extension of WGAN is WGAN-GP Gulrajani et al.) 2017 which added a new term in the loss that penalised the gradient norm of the discriminator w.r.t. the discriminator's input, providing an altornative to the weight clipping that was leading to the generator retaining the real data points and adding Gaussian noise to fill the gaps. VEEGAN: VEEGAN [Srivastava et al., 2017 jointly trains a generator and a novel reconstructor network in order to avoid mode collapse. The roconstructor learns to map the real data distribution to Gaussian random noise, approximating the inverse of the generator and encouraging the generator to map the noise distribution back to the real data distribution.
(KL) divergence, Jensen-
4.7 Non-deep learning alternatives
While deep learning approaches for synthesising tabular data have gained significant traction, it is important to note that they are not always better than the statistical methods. Indeod, in certain scenarios, such meth- ods can deliver competitive utility performance with lower computational costs and easier syper-parameter tuning. Further, for use cases requiring strong privacy guarantees, non-deep learning models are often better at balancing the utility-privacy trade-off than their deep learning counterparts.
One example of a classical statistical model is Synthpop Nowok et al. 2016 which is able to preserve multivariate relationships by modelling each tabular data feature conditional on the previously synthesised feature values. Generating synthetic data sequentially in this way avoids the training instability often seen with GAN-based models. More recently. Watson et al. 2023 introduced Adversarial Random Forests (ARF), which are tree-based generators able to combine the adversarial functionality of GANs with the robustness of tree ensembles to ultimately produce high-utility data. Yet another application domain where non-deep learning models excel is the privacy-preserving synthesis. For instance, rather than trying to approximate the full joint distribution of the real data, the Adaptive and Iterative Mechanism (AIM) McKenna et all, 2022 directly optimisos for pre-defined statistical queries and adds noise to a set of marginals of the data in order to satisfy differential privacy, and finally generates samples that best explain the marginals.
Finally, there are also works that bridge generative modelling and tree- based methods. For instance, JolicoeurMaartinean et al. (024 show that methods traditionally relying on deep learning, such as score- based diffusion and flow-matching, can be implemented using XGBoost instead of neural networks. This approach shows improved statistical fidelity and diversity compared to deep learning baselines such as Tab-
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Diversity
Privacy
STa5y
Fidelity
CoDi
TaDDDPM
TableGAN
TabSyn
CUTS
Neural Spline Flows
PATE-GAN
JDGGD
MedGAN
GEM
GEM+
IT-GAN
TTA--GAN+
TabTransGAN
FinDiff
DP-MERF
DP-NTK
ITS-GAN
CTAB-GAT
AutoDiff
-TAA
TGAN
Alignment
Utility
TabPFN
CCTANN
TVAE
GreAT GOGGLE
TabuLa
C-DGM
GANBLR
DGM+DRL
TabPFGen
OCTGAN
CWGAN
Figure 3:
Visualisation of the surveyed models based on the requirements they address.
DDPM Kotelnikov al. 2023
particularly on small datasets. Building on this approach, Cresswell Kim 2024 address the scalability limitations of these tree-based models, proposing efficient implementations that enable scaling to larger datasets with larger number of features and samples.
5 Discussion and Future Directions
In this survey, identified five key requirements for effective synthetic data deployment, alongside relevant evaluation procedures and deep generative models, while categorising the latter by model architecture.
Related work. Previous surveys generally compare methods by the architecture-specffic properties of the models. For example, both Borisov al. 20244 and Davila R. al. 2025 group methods mainly by their ar- chitoctures, while also describing the necessary data transformation and regularisation techniques. Lautrup et al. 2024 provide an overview of the models proposed in the field and the metrics used to evaluate them, while not taking this requirement-centee and rescarchers in the field to find the perfect model and evaluation protocol for their needs. Further, they exclude diffusion-based and LLMed architectures. On the other hand, Wang et al. 2025 narrow the scope of their survey and focus specifically on methods for social and government sector applications, where balancing utility and privacy the key concern.
perspective which helps both newcomers and seasoned practitioners
Another related work is the survey by Jordon al. 2022.. which provides a valuable, high-level view of synthetic data across various modalities, including audio, image, video, time-series, and tabular data,
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without focusing specifically on the latter. However, with primary emphasis on privacy, their survey treats requirements such as utility and fidelity as secondary goals. Further, rather than reviewing in detail methods for generating the data, the authors offer a high-level description of what syuthetic data is and why it is useful to socicty, arguing, alongside SSavage 2023 that a general public understanding of these methods is crucial given their potential to contribule to data democratisation. While Jordon et al. 2022 advocate for systematic frameworks, they categorise methods primarily by application (e.g., private data release, fairness). Further, regarding tabular data, their work relies on GAN-based approaches and does not cover recent advancements such diffusion transformer-basee
architectures. Finally, van Breugel et al. 2024 review methods for improving data fairness and reducing bias. However, their work focuses on biomedically-relevant data (including molecular, tabular, and imaging data) and surveys foundation models able to creale such data via query-specific generation. Thus, rather than focusing on methods that generate full datasets intended to replace or augment real data (i.e., the focus of this survey), they review methods which generate single samples conditioncd on specific inputs (c.g., an answer in the form of an image to a medical question).
In contrast to these works, our survey distinguishes itself by providing comprehensive overview of the requirements specific to synthesising tabular data and their complex interdependencies. To this end, we offer a practical, high-level roadmap (Figure 1) to guide users in selecting appropriate models. We support this roadmap with granular decision-making tools, including: (i) a structured technical taxonomy offering architectural details (Section 4), (ii) method-related specifics such as mixed data type support, inference time, and scalability to sigh-dimensional data (as part of Table 1), and (iii) an overview on which requirements are addressed by each method (Figure 3). The latter is particularly valuable for refining model selection based roquirements that are too intertwined to be effectively captured in the initial high-level roadmap. Furthermore, we support this user-centric perspective by detailing evaluation protocols and metrics for each requirement (Section 3). Overall, this structure positions our survey as resource for both newcomers and specialists to select and evaluate models tailored to their specific application scenarios.
Future Directions. Tabular data generation is a rapidly evolving field still in its early stages. As illustrated in Figure 3 many early approaches have prioritised individual -bjpcclvesttypicalll utility or privacy- leading to highly specialised models that lack broad applicabílity. Note that the categorisation in Figure 3 should be interpreted as a reflection of each method's focus, rather than an exclusive capability. As discussed in Section 3.6. these requirements are deeply interconnected: they often overlap or trade-off against one another. For example, the methods associated solely with the privacy requirement are positioned as such because their core contribution is a privacy-presering mechanism. However, this does not implicitly suggest they lack utility (indeed, a synthesiser with very low utility would be useless any downst task), but rather that their innovations are driven by primarily addressing the privacy requirement. Similarly, the methods associated to the fidelity requirement focus on approximating the real data distribution, which often sets the foundation for achieving a high utility.
This fragmentation highlights a key challenge: the need for models that can balance multiple, often com- peting, requirements. Notably, aligmment has historically received limited attention but is now emerging as a crucial factor for generating realistic data. With the increasing deployment of generative models in real-world applications and the growing prominence of neurosymbolic Al and safe Al (d' Aviil Garcez et al., 2019 Giunchiglia et al. 2022). we anticipate that alignment will soon bocome a fundamental requirement in the field. Emerging approaches are already tackling this challenge. For instance, training-based meth like Stoian & Giunchiglia 2025 introduce new layers to guarantee constraint satisfaction and improve utility,
while alternative directions focus on developing methods that do not require retraining, such as the work in Scassola et al. 2025b which proposes a zero-shot framework utilising soft constraints to approximate the conditional distribution. Moreover, the Figure reveals a striking gap: no existing model successfully integrates all the core requirements we consider. As the field matures, we expect new requirements will emerge, and the hybridisation of techniques will drive the development of more versatile models. Bridging these gaps will be essential for advancing the field and enabling broader, more reliable applications of tabular data generation, potentially expanding to complex multi-table relational data settings recently explored by Scassola et al. 2025a
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Broader Impact Statement
This survey captures current trends in deep generative modelling for tabular data synthesis, offers new perspective what makes synthetic data practically useful, and outlines key steps loward achieving such goal. We emphasise that, while existing methods address different requirements (e.g., alignment, utility, privacy, and fidelity), further progress toward developing approaches that simultancously meet multiple requirements will increase their impact in real-world applications. In particular, we highlight the importance of incorporating domain knowledge enhance the quality of synthetic data and encourage its integration in future deep generative modelling approaches for synthesising tabular data. It is important, however, ensure that such background knowledge does not embed user-specific biases or characteristics, this could raise privacy concerns. Provided this condition is met, injecting domain knowledge into generative models does not pose any direct negative impact.
Acknowledgments
Mihaela Cätälina Stoian was supported by the EPSRC under the grant EP/T517811/1.
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A Appendix
In this Appendix, we provide the formulae for each of the metrics presented in Table 2 We denote by and the sampled population size (i..., the total number of rows in dataset) and the number of features (i.e., the total number of columns in a dataset), respectively. Moreover, I(-) is the indicator function, which returns 1 if the condition inside the parentheses is true, and 0 otherwise, We also denote the true positives, true negatives, false positives, and false negatives by TP, TN, FP, and FN, respectively. The sets R and 8 represent the real and synthetic datasets, respectively.
Utility
TP + TN TP+TN + F
Accuracy
(1)
2 Precision Recall
F1-score
(2)
Precision + Recall
where Precision
TP TP4FP and Recall TP+FN
TP
N
Root mean square error (RMSE)
[yk - 9.)3,
(3)
N
where yi and 0. denote the actual (i.e., ground-truth) target value and the predicted target value for the i-th sample, respectively.
Explained variance 1 Var(y - y) Var(y)
where y and represent arrays of actual and predicted values, respectively, and Var(-) represents the variance of set of values.
Epistomic parity = |241
Σ [[f((S)) = f(D)),
(5)
wEll
where D is the universe of datasets, f is finding function D + {0, 1), and S, represents the synthetic dataset obtained by training a generator with seed u drawn from the set of random seeds U.
Alignment
N Constraint violation rate (CVR) = Σ I(sample violates any constraint)
1
(6)
N
Constraint violation coverage (CVC) #constraints violated by any of the N samples
(7)
#constraints
Sample-wisc constraint violation coverage (sCVC) = N Σ
#constraints violated by sample #constraints
(8)
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Fidelity In what follows, (i) F represents the cumulative distribution function of given feature in dataset D, (ii) (-r(- denotes the Kullback-LLeibler (KT.) Divergence, measuring how one probability distribution diverges from a second, while P and Q denote the probability distributions of the real and synthetic data, respectively, (iii) M is the mixture (average) distribution between P and Q, and (iv) 0 represents the parameters of the model trained synthesise data.
Further, sup, is the supremum (i.e., the least upper bound of set of values over all possible x), and Ls(i, represents the mutual information between features i and j in dataset D. Finally, Ps.ij is the correlation coefficient (e.g., Pearson) between features and in dataset D.
Feature wise evaluation metrics:
Wasserstein distance = [FR(x) - Fs(x) dz
(9)
Kolmogorov-Sminn test statistic sup (F((z) Fs(x))
(10)
Jensen-Shannon divergence DxI(PIIM) DKL (Q
(11)
Σ [P(x) Q(a))
Total variation distance
(12)
2. Pair-wise evaluation metrics:
RMSE differences in mutual information
(IR(i.)) Is(i,)))
(13)
D2 i.
MAE differences in mutual information
Σ [R((,,) 1s(i,5)
(14)
D>2
2 Correlation difference D(D - 1)
Σ
|RR,35 - ps.ú
(15)
icj
3. Joint evaluation metries:
Likelihood fitness score
1
Σ
log Px
(16)
R
XER
a-Precision
Σ 11 [xx, e supp (u)).
(17)
S
x,ES
where supp.(R) the minimum volume subsct of supp(R) that supports a probability mass of a.
Density [8]
E1 R s.t. |x, x,|| (N.))
(18)
x,ES
where (xD+ denotes the distance from x, the k-th nearest neighbour of x,-
Clipped density unnorm
1))
Clipped density = min
(19)
Clipped density
where:
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Clipped density unnorm
1
Σ
min
1
Σ X,ER
1(1x, x, s Blo(x.)).1)
(20)
k
x,E8
Clipped density real
1
Σ XER
min
Σ X.ER
T([|= noc-xx, x, S Rx(x,)).
(21)
R
k
and the elipped radius (x,,,) is defined as the minimum of (X,) which is the distance from X, to its k-th nearest neighbour, and the median of such distances across the dataset:
Rx(x.) = min (NND&(x,), Media X E R.))
(22)
Privacy
AUCROC (for membership attacks) P(score(member)
moorenon--membe)
(23)
TP TP + FP
Precision (for attribute disclosure attacks)
(24)
TP TP+FN
Recall/Sensitivity (for altribule disclosure allacks)
(25)
Distance to the closest record (DCR) = min dist((x,,x)) for Xs ES x,
(26)
minx, ER dist X,)
Ncarest neighbour distance ratio (NNDR)
for x, E S ming,eR (x.) dist (x,st(x;;x))
(27)
k-anonymity =
Σ X,ER
I([xx' : u = u6i 1 k))
(28)
R
where v represents the values of the quasi-identifier attributes (i.e., attributes that can be combined to uniquely identify an individual) for a given sample x.
Diversity
8-Recall =
Σ
T(x, E (u))
(29)
R
X,ER
where supp(S) is the support of S and supp:(S) is the minimum volume subset of supp(S) that supports a probability mass of 3.
Coverage
Σ
I(Ex, E S s.t. ||x, -xll < (N,))xx,),,
(30)
R
X.ER
where (x.) denotes the distance from x, to the k-th nearest neighbour of x
Σ min {
< 1(1x, x.Il NND.(x.)).1))
Clipped Coverage
(31)
R
X.ER
X.ES
where g(-) is calibration function such that the metric scales linearly with the proportion of valid samples
(see Salvy et al. 2025
26


Reviews:
[{"review_id": "iUp3Dk6qkH", "reviewer": "Reviewer_fM1d", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper surveys the literature on tabular data generation. The authors identify four key requirements that define high-quality synthetic tabular data: utility (the usefulness of generated data for downstream tasks), alignment (the ability to respect domain constraints and semantics), fidelity (the preservation of statistical properties and complex feature relationships), and privacy (the protection of sensitive information). Based on these dimensions, the paper reviews a wide range of generation techniques and discusses representative methods that are presented as addressing each of these requirements.", "claims_and_evidence_yn": "No", "claims_explanation": "While the paper aims to present a comprehensive survey with a clear categorization of tabular data generation methods, several aspects of the proposed taxonomy are confusing and, in my view, should not be presented in their current form.\n\nFor example, in the model types categorization (as illustrated in Figure 1), the authors introduce \"layer-based\" models as a separate category. However, most models listed under other categories (e.g., GANs, diffusion models) are also inherently layer-based. The resulting classification appears inconsistent and raises questions about the rationale and usefulness of such a distinction.\n\nSimilarly, the assignment of methods to the proposed requirement categories (utility, privacy, alignment, and fidelity) is difficult to interpret and risks being misleading. The conceptual relationships among these requirements are not clearly articulated; in practice, some of them tend to reinforce each other (e.g., higher fidelity often supports higher utility), while others are frequently in tension (e.g., the privacy–utility trade-off). Given this, it is unclear how to interpret the categorizations shown in Figure 2. For instance, some methods are presented as satisfying only “privacy”, while others “privacy and utility,” etc., even though any method that claims to be privacy-preserving should, by design, aim to balance privacy and utility at the same time, rather than addressing one in isolation. As currently presented, such categorizations may therefore oversimplify the methodological landscape and obscure rather than clarify the contributions of each approach.", "audience_yn": "Yes", "audience_explanation": "This paper presents a reasonably comprehensive (to the best of my knowledge) overview of existing tabular data generation methods, which should be relevant and of interest to the community. Furthermore, the attempt to outline key requirements for synthetic tabular data and describe how current approaches meet them to varying degrees may help clarify important considerations for future work in tabular data generation.", "requested_changes": "The core categorization framework of the survey requires substantial restructuring. In its current form, several classification choices are confusing and risk misleading readers. Specifically:\n\n- Model type taxonomy (e.g., the inclusion of layer-based models as a separate category) should be revisited, as this label appears to apply broadly to most architectures included in other categories (such as GANs and diffusion models), making the distinction unclear and of limited value.\n\n- Categorization of methods under the four requirement dimensions (utility, privacy, alignment, fidelity) needs clarification and potential redesign. The conceptual boundaries and relationships among these requirements are not well defined, yet the survey assigns methods to single or combined categories in a way that is difficult to interpret and may oversimplify or misrepresent the inherent trade-offs (e.g., privacy–utility) or natural alignments (e.g., fidelity–utility).\n\nTo improve clarity and rigor, I recommend that the authors revise the categorization scheme, provide an explicit justification for category definitions, and ensure that method placement reflects well-differentiated and conceptually well-defined criteria.", "broader_impact_concerns": "I am not aware of any specific ethical concerns that require more detailed discussion.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "cnPfSIkoQV", "reviewer": "Reviewer_NnVd", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "## Contributions\n\nThe paper reviews tabular synthetic data generation methods. They group these based on requirements \"Utility\", \"Alignement\", \"Fidelity\", and \"Privacy\", and later based on underlying modelling method.\n\n## Strengths\n\n1. I applaud the idea of a user-centric survey that could help practitioners generate and evaluate their models.\n2. The method survey is quite extensive, and the in-text explanations of individual works generally good.\n3. Although there are surveys out there, a new survey that keeps up-to-date with recent methods (e.g. in diffusion) is valuable.\n\n## Weaknesses\n### 1. Contribution and structure.\n\nAuthors write in the introduction:\n\n> This survey takes a unique stance and analyses models and evaluations methods alike from the point of\nview of the user, categorising them on the ground of the requirements they primarily address and measure:\nutility, alignment, fidelity, and privacy\n\nI do not agree that the current paper provides sufficient insight or recommendations to help users choose a model, generate data, or evaluate the data. For example, Figure 1 contains high-level ideas of models, but without additional explanations this figure is not comprehensible. Similarly, there are so many methods that a user could choose from---it would have been great if there was more structure in which they are presented (e.g. a decision tree for methods, or at least multiple axes on which different methods are compared such that the user can immediately see which methods would apply to their setting)\n\nMore importantly, I do not agree with the general structure of the paper. The Sections 3-6 (e.g. \"Utility\", \"Alignment\") suggest authors will focus on metrics/requirements, but then Section 3.2, 4.2, 5.2, discuss methods. It seems authors are of the opinion that generative models are designed for one metric (e.g. utility), but this is not true---methods hopefully optimize for multiple metrics (at least 1 and 3 at the same time, privacy is a separate objective and alignment can be targeted explicitly or implicitly). There are also trade-offs that make it unwise for users to focus on one requirement, ignoring another. This is also reflected in Table 2's indication that methods have a \"Primary requirement\". The authors do seem to acknowledge the overlap in Figure 2, but here too methods like \"PATE-GAN\" are not in the \"fidelity/utility\" circles---even though such methods are clearly designed to also be close to real data. Having separate Metrics and Methods sections would in my opinion be more appropriate (where methods can be split up according to Figure 2). This would also get rid of Section 7, which is a bit of a non-section as the methods could easily be applied to e.g. fidelity.\n\n\n### 2. Metrics\n\nBeyond the structure, the discussion of metrics is in general, insufficient. References are missing, in text as well as from Table 1. The \"Alignment\" requirement is strictly weaker than \"Fidelity\"---this is fine, but the relationship between the two should be highlighted. These relationships also consist of trade-offs, e.g. between \"privacy\" and \"fidelity\", which is not acknowledged. \n\nThere is also more work on joint-distribution fidelity, e.g. (Improved) Precision and Recall, Density and Coverage, or Alpha-Precision and Recall. These are more modern and well-cited, and I think they are valuable to capture high-dimensional data quality. At last, there is also a requirement that is not mentioned in the paper: diversity/coverage. This is important, e.g. for the mentioned example of generating \"rare data\".\n\nAlaa, A. M., van Breugel, B., Saveliev, E., & van der Schaar, M. (2022). How Faithful Is Your Synthetic Data? Sample-Level Metrics for Evaluating and Auditing Generative Models. International Conference on Machine Learning (ICML), 290–306.\n\nGulrajani, I., Raffel, C., & Metz, L. (2019). Towards GAN Benchmarks Which Require Generalization. 7th International Conference on Learning Representations, ICLR 2019.\n\nKynkäänniemi, T., Karras, T., Laine, S., Lehtinen, J., & Aila, T. (2019). Improved Precision and Recall Metric for Assessing Generative Models. Advances in Neural Information Processing Systems, 32. https://github.com/kynkaat/improved-precision-and-recall-metric.\n\nNaeem, M. F., Oh, S. J., Uh, Y., Choi, Y., & Yoo, J. (2020). Reliable Fidelity and Diversity Metrics for Generative Models. In H. D. III & A. Singh (Eds.), Proceedings of the 37th International Conference on Machine Learning (Vol. 119, pp. 7176–7185). PMLR. http://proceedings.mlr.press/v119/naeem20a.html\n\nSajjadi, M. S. M., Bachem, O., Lucic, M., Bousquet, O., & Gelly, S. (2018). Assessing Generative Models via Precision and Recall. In S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, & R. Garnett (Eds.), Advances in Neural Information Processing Systems (Vol. 31).\n\n\n### 3. Low-level structure\n\nBesides the high-level structure, the article's structure can be improved more granularly. For example, Section 6.2.; starts with \"AE and GAN-based models\", then continues with \"GAN-based models\". Similar in Section 4.2, and 5.2 has similar issues (diffusion-based, followed by more diffusion paragraphs). \n\n### 4. Contributions/related work\n\n> [this survey] offers a new perspective on what makes synthetic data practically useful,\n\nIt would be helpful if the authors specify what exactly this new perspective is compared to existing surveys. They mention on p.12 some related work, but there are much more related surveys, e.g. (Jordon et al, 2022), (Savage et al, 2023) or (Van Breugel et al, 2024). I do see value in a new review, especially since the popularity of diffusion models (which these previous reviews hardly capture).\n\nJordon, J., Szpruch, L., Houssiau, F., Bottarelli, M., Cherubin, G., Maple, C., Cohen, S. N., & Weller, A. (2022). Synthetic Data—What, why and how? (No. arXiv: 2205.03257). https://doi.org/10.48550/arxiv.2205.03257\n\nSavage, N. (2023). Synthetic data could be better than real data. Nature. https://doi.org/10.1038/D41586-023-01445-8\n\nvan Breugel, B., Liu, T., Oglic, D., & van der Schaar, M. (2024). Synthetic data in biomedicine via generative artificial intelligence. Nature Reviews Bioengineering, 2(12), 991-1004.\n\n\n### 5. Writing\n\nWriting could be improved throughout. Some examples:\n\n\n>  [p.2] While above we have the goal for standard generative modelling,\nwe know that different use cases can lead to additional requirements, which lead to different goals for the\ngenerative task.\n\nBit vague, please rephrase.\n\n\n> [p.2] ..., i.e., stating which samples are admissible and which are not, the goal is to learn the parameters\nθ of a generative model such that (i) the model distribution pθ approximates pX, and ...\n\nPart \"(i) the model distribution pθ approximates pX\" is important for most requirements, so it can be removed here (it's already at the top of the page).\n\n\n> [p.4] 3[.0] Utility\n\nUtility is important because it's easy and targets the downstream task directly. This paragraph is quite unclear and I suggest focusing on the core---it's ease of use---instead of e.g. the tangent of rare data.\n\n> [p.7] 5[.0] Fidelity\n\nAgain, these \"Section.0\" paragraphs can be shortened and more to the point as it's currently a bit unclear what the authors want to achieve with these paragraphs.", "claims_and_evidence_yn": "No", "claims_explanation": "The grouping is the primary contribution, yet this grouping is not motivated, and in my opinion, incorrect (see Weakness 1).", "audience_yn": "No", "audience_explanation": "The paper has potential and could indeed be interesting to a large group of practitioners if the recommendations were specific (e.g. if their was a decision tree or very clear structure on which practitioners could base their generation and evaluation protocols). In the current form, however, it will be difficult for practitioners to understand what method to choose.", "requested_changes": "See the weaknesses above. In particular, for me the following are vital to acceptance:\n1) the trade-off between requirements\n2) inclusion of diversity requirement\n3) regrouping that acknowledges this trade-off. This probably means a general restructuring of the paper into metrics versus methods\n\nNot essential but highly recommended\n1) more literature on metrics\n2) clearer structure for practitioners that can truly help them match their setting with the best method\n3) cleaner paragraph structure and writing\n4)", "broader_impact_concerns": "No concerns", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "UiWJxkNim3", "reviewer": "Reviewer_B4TN", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper is a survey of deep learning methods for synthetic tabular data generation, and metrics to evaluate these methods. Both metrics and methods are grouped by the goal they aim for. The paper considers four goals: utility, alignment, fidelity and privacy. Utility is measured by the performance of downstream predictive models. Alignment refers to domain-specific constraints the synthetic data should follow. Fidelity is measured by the statistical similarity of the synthetic and real data, or similarities of their marginals. Privacy is the vulnerability of the synthetic data to various attacks such as membership inference or attribute disclosure that undermine the privacy of the data subjects.", "claims_and_evidence_yn": "No", "claims_explanation": "The paper is missing discussion on some important works. The scope defined in the paper is narrow in some aspects, and excludes discussion that would be beneficial for readers, especially those not familiar with tabular synthetic data generation. See Requested Changes for details.", "audience_yn": "Yes", "audience_explanation": "The paper is a decent survey of deep synthetic data generation methods for tabular data. Many surveys on synthetic data generation exist, but I'm not aware of one that looks at tabular data in general, including both generation and evaluation methods. The paper's categorisation based on the goal of of the generator or metric is also both novel and useful.", "requested_changes": "**Important Changes**\n\nThe definition of utility in the paper (predictive performance) is narrow. Synthetic data could be used for many other purposes than machine learning. For example, Rosenblatt et al. (2023) and Perez et al. (2024) evaluate whether statistical inferences can be reproduced from synthetic data. These should be mentioned.\n\nThe focus on deep models is limiting. It is understandable to limit the scope, but there are several very good non-deep tabular data generators, especially with differential privacy, that are hidden by this focus. Examples include ARF (Watson et al. 2023), Synthpop (Nowok et al. 2016) and AIM (McKenna et al. 2022). While these do not need to be discussed in the same detail as the deep learning models, it would be beneficial to tell readers that deep learning models are not always the best tabular data generators, and give some pointers to alternatives.\n\nIn-scope methods or evaluation metrics that should be included:\n- TPR at low FPR (Carlini et al. 2022) should be mentioned as a MIA evaluation metric.\n- There is a line of work on synthetic data fidelity and diversity metrics that is not discussed. See Salvy et al. (2025) and the metrics they compare with. The original papers focus on image data, but these metrics can be used with tabular data, and have been used by for example Kotelnikov et al. (2023).\n- TabPFNv2 (Hollman et al. 2025) can generate synthetic tabular data.\n- GEM (Liu et al. 2021), DP-MERF (Harder et al. 2021) and derivatives of DP-MERF (Yang et al. 2024 and their references) are differentially private deep generative models.\n\n**Minor changes**\n- Not clear what \"Generation Time\" column in Table 2 is based on, and precisely what \"slow\", \"fast\" etc. mean.\n- The mathematical description of a tabular dataset is unusual and hard to understand. A more understandable description would be defining datapoints as tuples, and a dataset as a list (or vector) of tuples.\n- The definition $X \\in \\cup\\_{j=1}^K \\mathbb{D}^j$ in the beginning of page 2 does not make sense with the surrounding definitions. A datapoint is a tuple where each element is from one of the $\\mathbb{D}^j$ sets, not a single element from the union.\n- The term \"fidelity\" has an established but different meaning in synthetic data evaluation literature (for example Naeem et al. 2020).\n- On the alignment definition: it is possible for real data to contain erroneous values. In the given example, the minimum and maximum haemoglobin levels could swapped due to human error, so the statement that real data do not contain such values is not always correct.\n- Membership attacks are usually called membership inference attacks.\n- Avoid rotated tables if at all possible. They are annoying to read.\n- Table 2 should be closer to the introduction where it is referenced.\n- Rows in Table 1 are not horizontally aligned, for example compare the second and third columns of the fourth row.", "broader_impact_concerns": "No ethical concerns.", "additional_comments": "References:\n- Carlini et al. (2022) \"Membership Inference Attacks From First Principles\" IEEE Symposium on Security and Privacy\n- Harder et al. (2021) \"DP-MERF: Differentially Private Mean Embeddings with Random Features for Practical Privacy-preserving Data Generation\" AISTATS\n- N. Hollman et al. (2025) \"Accurate predictions on small data with a tabular foundation model\" Nature\n- T. Liu et al. (2021) \"Iterative Methods for Private Synthetic Data: Unifying Framework and New Methods\" NeurIPS\n- McKenna et al. (2022) \"AIM: an Adaptive and Iterative Mechanism for Differentially Private Synthetic Data\" Proceedings of the VLDB Endowment\n- M. F. Naeem, S. J. Oh, Y. Uh, Y. Choi, J. Yoo (2020) \"Reliable Fidelity and Diversity Metrics for Generative Models\" ICML\n- Nowok et al. (2016) \"synthpop: Bespoke Creation of Synthetic Data in R\" Journal of Statistical Software\n- I. Perez et al. (2024) \"Does Differentially Private Synthetic Data Lead to Synthetic Discoveries?\" Methods of Information in Medicine\n- L. Rosenblatt et al. (2023) \"Epistemic Parity: Reproducibility as an Evaluation Metric for Differential Privacy\" Proceedings of the VLDB Endowment\n- Salvy et al. (2025) \"Enhanced Generative Model Evaluation with Clipped Density and Coverage\" arXiv:2507.01761\n- Yang et al. (2024) \"Differentially Private Neural Tangent Kernels (DP-NTK) for Privacy-Preserving Data Generation\" Journal of Artificial Intelligence Research\n- Watson et al. (2023) \"Adversarial Random Forests for Density Estimation and Generative Modeling\" AISTATS", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)