Leveraging Diffusion Model as Pseudo-Anomalous Graph Generator for Graph-Level Anomaly Detection
Authors: Jinyu Cai
Yunhe Zhang
Fusheng Liu
See-Kiong Ng
Venue: ICML 2025 spotlightposter (2025)
Keywords: Anomaly Detection
Diffusion Model
Graph Neural Network
Primary area: general_machine_learning->unsupervised_and_semisupervised_learning

Abstract: A fundamental challenge in graph-level anomaly detection (GLAD) is the scarcity of anomalous graph data, as the training dataset typically contains only normal graphs or very few anomalies. This imbalance hinders the development of robust detection models. In this paper, we propose **A**nomalous **G**raph **Diff**usion (AGDiff), a framework that explores the potential of diffusion models in generating pseudo-anomalous graphs for GLAD. Unlike existing diffusion-based methods that focus on modeling data normality, AGDiff leverages the latent diffusion framework to incorporate subtle perturbations into graph representations, thereby generating pseudo-anomalous graphs that closely resemble normal ones. By jointly training a classifier to distinguish these generated graph anomalies from normal graphs, AGDiff learns more discriminative decision boundaries. The shift from solely modeling normality to explicitly generating and learning from pseudo graph anomalies enables AGDiff to effectively identify complex anomalous patterns that other approaches might overlook. Comprehensive experimental results demonstrate that the proposed AGDiff significantly outperforms several state-of-the-art GLAD baselines.

Leveraging Diffusion Model as Pseudo-Anomalous Graph Generator for Graph-Level Anomaly Detection
Jinyu Cai Yunhe Zhang? 2*
Fusheng Liu
See-Kiong Ng
Abstract
crucial across numerous domains, from detecting abnormal patterns in social networks (Yu et al., 2016; Zhang et al., 2025; Qiao & Pang. 2023) to identifying anomalous pro- teins in biological systems (Li et al., 2022). Unlike node- or edge-level anomaly detection (Duan et al., 2023; Qiao et al., 2024a;b; Pan et al., 2025), GLAD poses unique challenges as it requires modeling complex topological and geometric structures at the entire graph level.
A fundamental challenge in graph-level anomaly detection (GLAD) is the scarcity of anomalous graph data, as the training dataset typically con- tains only normal graphs or very few anoma- lies. This imbalance hinders the development of robust detection models. In this paper, we propose Anomalous Graph Diffusion (AGDiff). framework that explores the potential of dif- fusion models in generating pseudo-anomalous graphs for GLAD. Unlike existing diffusion- based methods that focus on modeling data nor- mality, AGDiff leverages the latent diffusion framework to incorporate subtle perturbations into graph representations, thereby generating pseudo- anomalous graphs that closely resemble normal ones. By jointly training a classifier to distin- guish these generated graph anomalies from nor- mal graphs, AGDiff learns more discriminative decision boundaries. The shift from solely model- ing normality to explicitly generating and learning from pseudo graph anomalies enables AGDiff to effectively identify complex anomalous patterns that other approaches might overlook. Compre- hensive experimental results demonstrate that the proposed AGDiff significantly outperforms sev- eral state-of-the-art GLAD baselines.
The evolution of GLAD methods has witnessed several key developments. Classical graph kernel methods, such as the Weisfeiler-Lehman kernel (Shervashidze et al., 201 1), random walk kernel (Vishwanathan al., 2010), have estab- lished a foundation for GLAD by computing graph similar- ity matrices based structural features. These approaches excel at capturing local topological patterns, but typically struggle with computational complexity. Recent deep learn- ing based GLAD methods have emerged in both unsuper- vised and supersupe paradigms. Unsupervised meth- ods typically employ graph neural networks (GNNs) (Kipf & Welling, 2017: Xu et al., 2019; Huang et al., 2023; Wan et al., 2024; Tu et al., 2025) to learn graph-level features for anomaly detection, with techniques such as one-class clas- sification (Ruff et al., 2018; Qiu et al., 2022; Zhang et al., 2024), information bottleneck (Liu et al., 2023a), knowledge distillation (Ma et al., 2022), and graph reconstruction (Kim et al., 2024) to learn normality patterns without labeled anomalies. supeviuper approaches (Zhang et al., 2022: Xu al., 2024) generally leverage limited graph anomalies to train a classifier the anomaly detector. Even though only small fraction of labeled anomalies are available, supervupe approaches have demonstrated remarkable performance improvement in detecting graph anomalies.
1. Introduction
Graph-level anomaly detection (GLAD) (Akoglu et al., 2015; Qiao al., 2024a; Liu al., 2024b; Cai et al., 2024d) focuses the fundamental challenge of identifying irregu- larities in graph-level data, where anomalous graphs signifi- cantly deviate from the normal graph distribution. GLAD is
Despite these advancements, several critical limitations per- sist in existing approaches. Unsupervised methods focus on modeling normal graph distributions, they generally strug- gle to distinguish intricate subtle anomalies, especially those near the boundaries of normal graphs, due to the lack of explicit supervised information. On the other hand, semi-supervised approaches can leverage limited labeled anomalies to enhance decision boundary learning. How- ever, their effectiveness is constrained by the scarcity and diversity of labeled anomalous graphs, which limits their
'Institute of Data Science, National University of Singapore, Singapore 'Department of Computer and Information Science, SKL-IOTSC, University of Macau, Macau, China. Correspon- dence to: Yunhe Zhang <zhangyhannie@ aaaaaaaiiiiiimmaammmmm...... gmail.com>.
Proceedings of the 42nd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Leveraging Diffusion Model Pscudo-Anomalous Graph Generator for Graph-Level Anomaly Detection
Pre-Training
Joint Training
Latent Diffusion
3
Diffusion Forward Process
Zo
ZT
Perturbation Condition
Encoder
--
Original Graphs g
X (7 1) times
D
Denoising Network Eg
Zo
2 2T-1
Decoder
Pseudo Anomalies
Anomaly Detector
hg(C)
GNN Backbone
Prediction
h (G)
Graph-level Representations
MLP Predictor
Figure 1. An illustration of the proposed AGDiff framework. The framework consists of three main components: (1) Pre-training, (2) Latent diffuusion-ai based greudo-anomalon graph generation, and (3) Anomaly detector. The pre-training phase learns structured latent space via a reconstruction model. The latent diffusion process generates pseudo-anomalous graphs by perturbing latent embeddings through a forward diffusion process a reverse denoising process. Finally, the anomaly detector distinguishes between normal generated pscudo-anomalous graphs through joint training.
generalizability
unseen anomaly types.
2. We propose latent diffusion process with perturbation conditions to generate pseudo-anomalous graphs without relying on any labeled anomalies for improving decision boundary learning.
To address these challenges, we propose Anomalous Graph Diffusion (AGDiff), a novel framework (see Figure 1) that leverages the generative capabilities of diffusion models to generate diverse sveudo-anomaloo graphs for GLAD. By introducing a conditioned latent diffusion process within well-trained graph representation learning model, AGDiff ensures the preservation of essential graph properties while imposing controllable perturbations in the latent space. Ad- ditionally, AGDiff employs joint training paradigm that simultancously optimizes pseudo-anomalous graph gener- ation and anomaly detection. Our algorithm analysis (in Appendix A) highlights the advantages of AGDiff over traditional reconstruction-bint based methods by demonstrating that leveraging diverse pseudo-anomalous graphs enables more robust and refined decision boundary for anomaly detection. By bridging the gap between generative modeling and discriminative learning, AGDiff offers a generalizable solution to the fundamental challenges of GLAD.
3. We demonstrate the superiority of AGDiff across exten- sive comparisons with state-of-the-art GLAD baselines on diverse graph benchmarks.
2. Related Work
2.1. Graph-level Anomaly Detection
Graph-level anomaly detection (GLAD) (Akoglu et al., 2015; Qiao et al., 2024a; Cai et al., 2024b) aims to identify graphs whose structural or attribute patterns deviate from the majority, with widespread real-world applications fraud detection, bioinformatics, and cybersecurity. Traditional approaches, such graph kernels (Borgwardt & Kriegel, 2005; Vishwanathan et al., 2010; Shervashidze et al., 201 1), struggle to model the intricate dependencies within graph data due to their reliance on hand-crafted features. In recent years, the emergence of GNNs (Kipf Welling, 2017; Xu et al., 2019;
The primary contributions of this work are as follows:
We propose AGDiff, the first framework that explores the potential of diffusion models to mitigate the anomaly scarcity challenge in GLAD.
al., 2023: Liu et al., 2023b; Cai al., 2024a;c) has substantially advanced GLAD via their ex- pressive graph representation learning capabilities. Latest
2

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Leveraging Diffusion Model Pscudo-Anomalous Graph Generator for Graph-Level Anomaly Detection
GLAD approaches have explored knowledge distillation for global-local anomaly identification (Ma et al., 2022), graph transformation learning to mitigate representation col-
ods (Wolleb et al., 2022: Tebbe & Tayyub, 2024; Li et al., 2024) primarily focus modeling normality and expect anomalies to emerge naturally reconstruction outliers, pre- supposing that anomalies deviate significantly in topology or node features. Such an assumption falters when anomalies are inherently subtle, especially in graphs where localized irregularities can be easily "diluted" by global reconstruc- tion. Different from the existing approaches. we propose to leverage diffusion models generator through controlled perturbations introduced dur- ing the diffusion process. We expect the generated pseudo graphs to resemble the normal graphs, so that they can provide explicit supervision for learning a robust anomaly detection model.
lapse (Qiu et al., 2022), counterfactual graph generation for robust detection (Xiao et al., 2024a), spectral analysis to capture global graph anomaly properties (Dong et al., 2024), and explainable learning for interpretable anomaly detec- tion (Liu et al., 2023a), etc. Additionally, superviiee learning (Zhang et al., 2022) is also studied to alleviate the data imbalance problem in GLAD.
aseudooanomalle graph
Despite these advancements, existing GLAD methods still face sigmificant limitations. For example, the reconstruction flip phenomenon identified by Kim et al. (2024) reveals that the common assumption in existing approaches, i.e,, anomalies necessarily exhibit higher reconstruction errors, is not universally applicable. Moreover, existing approaches are trained with only normal graph data or just a small set of anomalies, which limits their generalizability to un- seen anomalies. Consequently, in the proposed AGDiff framework, we aim to adaptively generate diverse pseudo- anomalous graphs to enhance the capacity to detect subtle and complex anomalies while mitigating data imbalance issues. Furthermore, the generative process inherently im- proves interpretability by revealing how -nnumlos graphs are generated through controlled perturbations. Com- pared to other approaches, our method delivers a robust and interpretable solution for GLAD problems.
3. Preliminary
The diffusion model, e.g., denoising diffusion probabilistic model (DDPM) (Ho et al., 2020), is one of the generative model families, which typically contains a forward diffusion process that perturbs the original data X into a noisy sample x₂ by progressively adding Gaussian noise over T time steps, and a reverse denoising process that attempts to recover Xu from x, by removing the noise step-by-step. Specifically, the forward diffusion process is defined as:
Vo,X0 + v1 C.et, IO.,I)
(I)
Here, ā. = 1T a; = [1 -1 B;), where B; denotes the noise variance schedule that imposed at each time step.
2.2. Diffusion Model
The reverse denoising process can be understood as a series of learned denoising steps to recover the original data x from the noise sample Xt. At each time step t, X is reconstructed by:
Diffusion models (Ho et al., 2020; Song et al., 2021; Yang et al., 2023) have emerged as a new paradigm for generative modeling, wherein data are gradually corrupted through diffusion forward process and subsequently denoised through learned reverse process. Early work by Ho et al. (Ho et al., 2020) demonstrated that diffusion processes could capture digh-diiensional densities more effectively than traditional architectures such as GANs (Goodfellow et al., 2020; Wang et al., 2021; Cai et al., 2024e) and VAFS (Kingma, 2013). In the context of image anomaly detec- tion, diffusion-basee methods have demonstrated impres- sive capabilities in domains such industrial defect in- spection (Zhang et al., 2023; Tebbe & Tayyub, 2024) and medical anomaly detection (Wolleb et al., 2022; Bercea et al., 2024), as they excel by modeling intricate pixel-level dependencies, thereby enabling the identification of subtle deviations through the pixel-level reconstruction of images. Recent advances have investigated the diffusion frameworks for graph-structured data, demonstrating notable potential for tasks such as graph generation (Kong et al., 2023), node classification (Yang et al., 2024), and graph anomaly detec- tion (Li et al., 2024; Liu et al., 2024a; Xiao et al., 2024b).
1 Xt-1 Va
1 -
to(xe, 11) + Bz, (2) VI āi
Xx
where co t) is learnable noise predict function, B 1-or-1 and ~ NN I) is sampled from normal Gaus- sian distribution. The training of diffusion models revolves around learning the reverse process that can accurately re- cover data from the noisy representation, where the objective can be expressed as:
d,
min ox [[le cx 0113]
(3) After training the model, the original data x. can be recon- structed by iteratively removing predicted noise ea (x,, t) from x,.
4. Methodology
4.1. Problem Formulation
However, existing diffusion based anomaly detection meth-
Let g = (V,E) denote a graph where V represents the set of vertices and & C V V represents the set of edges.
3

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Leveraging Diffusion Model Pseudo-Anomalous Graph Generator for Graph-Level Anomaly Detection
Each graph G is characterized by its adjacency matrix A E {0. 1)xxn and node feature matrix X E R where [V] is the number of nodes and d is the dimension of node features. In an unsupervised GLAD problem (Akoglu et al., 2015; Qiao et al., 2024a), given a normal graph set 9 = {G1, Gg...., GN3 } is given by sampling from an unknown normal graph distribution Pnormal. Our goal is to learn an anomaly detection function f G + E that identifies graphs deviating from P nommal- Specifically, for a test graph Gres, we aim to estimate:
A) and attribute (denoted by X) information for graphs:
À = T
X -Z),,
(6)
where T-)) denotes S gmo i transformation function, and D(-) represents an MLP-basee decoder for attribute reconstruction. The model is optimized by minimizing:
prretriin = -p + +ee pedge + (XI.
N Σ (1 - * H(A,, A.)
(7)
f(Gua) = P(Gres & Paoenaal Guest)
(4)
While some semi-supervised methods (Zhang et al., 2022)
attempt to introduce a small fraction of real anomalies into training classifier as the anomaly detector, the scarcity and limited diversity of anomalies make challenging to generalize unseen anomalous patterns. Therefore, we curious whether the normality induced by normal graph distribution can be leveraged as special kind of "super- vised information" to facilitate the training of a more robust graph anomaly detector. In this work, we aim to generate a set of pseudo-anomaly graphs by introducing controlled perturbations for normal graphs under a latent diffusion framework. Then, we jointly train graph anomaly detector with the generation framework so that the decision boundary learning and the pseudo-anomalous graph generation can be mutually refined. We will describe the details of our framework in the following sections.
where H(-) denotes the binary cross-entrops loss for edge reconstruction, and the KL divergence term regularizes the learned distribution towards prior P(Z) II, (z,(0, I), which encourages a smooth and well-structured latent space and prevents the model from overfitting to a narrow or de- generate latent manifold (Kipf & Welling, 2016).
4.3. Generating Anomalous Graphs via Latent Diffusion
Building on a well-structured latent space that effectively captures normal graph patterns, we propose a novel ap- proach that utilizes latent diffusion models to generate pseudo-anomalous graphs. This approach represents a substantial departure from conventional diffusion-based anomaly detection methods, which typically aim to model the normality of data via diffusion models. Instead, we exploit the generative power of diffusion models to gener- ate diverse pseudo-anomalous graphs by introducing con- trolled perturbations during the latent diffusion process. The smooth and continuous geometry of the latent space pro- vides a foundation for this process, enabling the preservation of critical structural properties and meaningful deviations from normality. Our key insights are: (1) the continuous na- ture of the latent space makes it particularly suitable for the diffusion process, and (2) the asymptotic nature of the diffu- sion process allows ane-grained control over the deviation from normality.
4.2. Modeling Normality via Variational Inference
In the context of graph-level anomaly detection, one of the foundational challenges is the modeling of the normal graph distribution, as anomalies are typically defined as deviations from the normality learned from given normal graph set Gnormal- To achieve this, we first pre-train a graph represen- tation learning model aiming at capturing the normality of graphs. Particularly, we leverage variational inference to learn probabilistic mapping from graph space to continu- ous latent space, as it naturally provides a well-regularized manifold for subsequent perturbation- based anomaly gen- eration. For a given graph set G = {A, X). we approxi- mate the posterior distribution over the latent representation Z Raxd, as:
Given normal graph set G (X, we first obtain its latent representation Z E(X, A) through the pre-trained model. To generate controlled perturbations, we design conditional latent diffusion process that consists of two key components: a forward process that gradually adds noise to the latent representation, and a reverse process that learns to denoise while preserving essential graph properties. The for- ward process progressively corrupts the latent representation by injecting Gaussian noise over T time steps:
(Z A) II
g(z, X,A),
(5)
1=1
w.I.t g (2, X, A) N |4, diag(o;)),
where and are parameterized by μ GNN,, A) and log o = GNN, A), respectively. By using the reparameterization trick to enable gradient propagation, we sample Z = 4 or 0 where T ~ NO I). The reconstruc- tion process involves recovering both structural (denoted by
Z Varza vI aic 4 a~ C~N(O.,) I),
(8)
where zo is initialized by Z, and ā I a
[1 (1 - B,) determines the noise schedule through B..
4

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Leveraging Diffusion Model Pscudo-Anomalous Graph Generator for Graph-Level Anomaly Detection
This schedule is crucial it determines the degree of per- turbation at each step.
Algorithm 1 AGDiff
Input: Input graph set G, number of GIN layers K, learn- ing rate p. diffusion time steps T, training epochs Epochs.
A key challenge in generating -anuadll graphs is maintaining the balance between structural preservation and anomaly injection. To address this, we design a conditional reverse process:
Output: The anomaly detection scores.
1: Initialize the network parameters;
2: Pre-train the representation learning model by minimiz- ing Eq. (7);
1- (o Bv. va 2,
(9)
VI-a, at
3: Freeze the network parameters of the pre-trained model;
where co(2), t. c) is our conditional noise prediction net- work, 3 = -1 and ~ IO. The condition vector &e
4: for epoch to Epochs do
5: Sample mini-hatch of graphs from graph dataset 9;
is obtained via perturbation condition model To to add auxiliary noise information to the generation process:
6: Obtain latent embeddings Z from the pre-trained en- coder;
7: Perform forward diffusion process on Z via Eq. (8);
c= (2o)= = o (We + n) + be),
(10)
8: Obtain the condition vector via Eq. (10);
where 17 (0, 1) is Gaussian noise vector that intro- duces perturbations to the initial latent representation, and the learnable weight matrix We and bias vector be trans- form the perturbed representation to more expressive fea- ture space through a non-linear activation function (.). The condition vector is concatenated with the latent variable 2, at each denoising step introduce controlled variations during the diffusion process.
9: Generate pseudo-anomaloo embeddings Z through the reverse diffusion process via Eq. (9);
10:
Decode Z via pre-trained decoder to generate pseudo- anomalous graphs set G;
11:
Predict scores for the normal and generated pseudo- anomalous graphs via Eq. (12);
12: Jointly update the parameters of the latent diffusion model and anomaly detector by minimizing Eq. (14);
13: end for
The condition vector c is crucial for guaranteeing the gen- eration quality of pseudo graph anomalies. If we directly use the perturbed normal data (e.g., via random noise 7)) as pseudo anomalies, it would constrain the diversity of anomalous patterns the model encounters, as such pertur- bations are static and lack adaptability during training. In contrast, we propose to perturb the initial latent embedding through learnable perturbation transformation c, which injects additional variability into the latent diffusion process. The perturbations are learnable and dynamically adjusted during joint training with the anomaly detector. As the anomaly detector improves, the perturbation mechanism evolves and generates increasingly sophisticated and diverse pseudo anomalies to refine the decision boundary. This en- sures that the denoising network is conditioned to deviate from purely "normal" reconstructions and allows the model to be exposed to a broader spectrum of potential anomalies, thereby enhancing its robustness and generalization. The latent diffusion model is then optimized by minimizing:
14: Compute anomaly detection scores for test graphs via the trained classifier fo;
15: Return: The anomaly detection scores.
rare or even unavailable, as their reliance on labeled anoma- lies limits their capacity to generalize to unseen abnormal patterns. This challenge becomes particularly pronounced in real-world scenarios, where anomalies are inherently rare and diverse. To overcome this limitation, we propose a joint learning framework that leverages generated pseudo- anomalous graphs to facilitate the training of the anomaly detector. These pseudo-anomalove graphs serve as proxies for real anomalies, which enables the model to learn more robust, adaptive decision boundaries that capture subtle de- viations from normality.
In practice, we employ a GIN-based anomaly detector h.)-)) to distinguish between normal graphs and pseudo- anomalous graphs, which is defined by:
Lan = c, [||c- - co(2,, t, e)]
(11)
Through the conditional diffusion process, we can iteratively generate perturbed latent features žo, i.e., Z, + Z +
ha MLP(GIN(X, A)).
(12)
where h.)+) parameterized by Φ is comprised of GIN- based backbone network GIN and an MLP-based projec- tor MLP(-). We employ a following binary cross-entrops loss Lats to train the anomaly detector:
+ 2o for each graph. Therefore, the pseudo-anomalouu graphs can be obtained through the pre-trained decoder via: A TZZT) and x D()), where 2 (2) N 1-
4.4. Detecting Anomalies from Subtle Deviations
Lek
Σ
(va log ha
Conventional semi-supervised GLAD approaches generally struggle in scenarios where real anomalous samples are very
GESUD
(13)
+ (1 va) log(1 - h (G))),
5

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Leveraging Diffusion Model Pscudo-Anomalous Graph Generator for Graph-Level Anomaly Detection
where 9 and & denote the normal and pseudo-anomalous graph sets, respectively. Note that we set yG VG G. and yG = 0, VG E 9 to train the anomaly detector. In particular, we jointly train the latent diffusion model and the anomaly detector by minimizing:
baselines such as SIGNET, MUSE, DO2HSC. In addition, potential optimizations such using parallel computation further enhance efficiency.
5. Experiments
L = Lets + Aaain
(14)
5.1. Experimental Setup
where À is the between two objectives. Cai guides the generation of pseudo graph anomalies, and Lek enhances the discrim- inative power of the anomaly detector. In the inference phase, we can obtain the anomaly score of each test graph sample via the trained anomaly detector. Algorithm sum- marizes the training procedure AGDiff. The joint learning framework offers several unique advantages:
that controls the trade-off
Datasets. We conduct experiments with two types of graph benchmarks, including
Moderate-Scale Datasets: MUTAG, DD, COX2, and ER MD. These datasets primarily consist of molecular graphs and bioinformatics networks, where nodes and edges represent molecular structures or protein interac- tions.
Large-Scale Imbalanced Datasets: SW-620, MOLT-4, PC-3, and MCF-7. Each graph in these datasets represents a chemical compound, with labels indicating whether it exhibits anti-cancer activity. The datasets are highly im- balanced as active compounds form only a small fraction of the total samples, which makes them well-suited for evaluating the robustness of anomaly detection methods in real-world, unbalanced settings.
1. The latent diffusion model learns to generate increasingly challenging pseudo- anomalies that explore the decision boundary of the anomaly detector.
2. The gradient of the detector directs the diffusion process toward generating more informative pseudo-anomalous samples.
3. The iterative refinement between generation and detec- tion leads to a more robust anomaly detector.
We describe the details about the datasets and their charac- teristics in Appendix B. Note that we follow the settings in existing works (Ma et al., 2022; Zhang et al., 2022; Liu et al., 2023a) to treat the minority class as the anomalous class to better align with real-world scenarios where anomalies often correspond to rare events or unusual patterns.
4.5. Computational Complexity Analysis
For dataset of N graphs, each with an average of nodes (feature dimension d), |E] edges, and latent dimension d,, the AGDiff framework operates in three phases:
Implementation Details. Due to the length limitation of the paper, please refer to Appendix C for the implemen- tation details of the experiment, including the data split, network architecture, typer-parameter setting, baseline set- ting, and computing resources.
1. Pre-training: An L-layer GIN is employed the back- bone network in the pre-training, where the overall com- plexity is O(N L(E]dd+mmd)) due to the message aggre- gation (l))) and feature transformation (O(md?) )).
2. Pseudo Anomaly Generation: This phase involves the computation of conditional vector (O(Nd)) and T- step latent diffusion process (O(NTmd?)) across all graphs.
Compared Baselines. To evaluate the effectiveness of the proposed AGDiff method, we compared with two types of GLAD baselines, including: (1) Graph Kernel Meth- ods: Phort-Path (SP) kernel (Borgwardt & Kriegel, 2005), Weisfeiler-Lehman (WL) kernel (Shervashidze et al., 201 1), NH (Hido & Kashima, 2009), Random Walk (RW) ker- nel (Vishwanathan et al., 2010), and (2) GNN-based GLAD Methods: OCGIN (Zhao & Akoglu, 2023), OCGTL (Qiu et al., 2022), GLocalKD (Ma al., 2022), iGAD (Zhang et al., 2022). SIGNET (Liu al., 2023a), MUSE (Kim et al., 2024), DO2HSC (Zhang et al., 2024).
3. Decoding and Anomaly Detection: Decoding involves the computation of node attributes and adjacency matri- ces from latent embeddings, which results in time com- plexity of (N Fldz) when we apply a negative sam- pling strategy in practice. The computational complexity of the anomaly detector is similar to the pre-training stage, i.e., (O(N + md)))). due to their similar network structure.
Evaluation Metrics. To evaluate the anomaly detection performance of each method, we utilize two widely adopted metrics: Area Under the Curve (AUC) and FI-Score. The experimental results are reported as the mean values and
Therefore, the overall computational complexity of AGDiff is approximately ((NL(E) [[Eld + md?) + NTm + 1)de + | Fl)d,, which is comparable with other state-of-the-art
6

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Leveraging Diffusion Model Pseudo-Anomalous Graph Generator for Graph-Level Anomaly Detection
Table Average AUCs and F1 -c-ooress with standard deviation (10 trials) four small and moderated graph datasets. The hest results are marked in bold, and "OM" denotes out -mmorr...
MUTAG
DD
COX2
ER
Method
AUC
F1-Scure
AUC
Fl-Score
AUC
Fl F1-Score
AUC
F1-Scure
SP (Borgwardt & Kriegel, 2005)
67.52=0.00
60.00=:0.00
82.73=00.00
76.09=0.00
54,08=00.00
49.32==0.00
40.92=0.00
37.74=0.00
WL (Shervasshide el ul., 2011)
60.00:10.00
89.12:10.00
81.57:100.0
74.64-10.0
49.02:10.00
10.19:10.00
45.71 37.04:10.00
NH (Hido Kashima, 2009)
79.97=0.40
76.00:1..00
81.61=0.32
73.91=0.65
61.41:0.82
16.4411.03
51.55
50.19:0.922
RW (Vishwanathan et al, 2010)
86.98 0.00
83.33++0.00
OM
OM
52.43++0.00
30.00+0.000
78.94
65. 65.96++0.00
OCGIN (Zhao & Akoglu, 2023)
74.66
62.95:10.00
66.5914.44
56.12:1.00
59.64415.78
47.95::0.00
4..6343.59
50. 50.94:11.89
OCGTL (Qiu al., 2022)
87.04 1.74
80.00=+0.00
77.52+00.43
71.65
60.42:+00.0
55.62++:.24
72.67=0.20
67.17=00.92
GLocalKD (Ma et al., 2022)
90,59:10.61
86.17:10.91
80,59:10.00
73.48
01.11.66666
51.24:10.00 60
78. 0.004
70.21
iGAD (Zhang ct al., 2022)
92.58: 1.25
85.20:+2.30
74.83=22.30
70.39:2.60
72.09:22.29
61.9411.00
80.56=22.57
74.57:22.45
SIGNET (Liu et al,, 2023a)
87.73++2.45
73.07:44.11
59.53:1:.45
56.76:t3.47
52.80:+2.53
20.24:1-4.2
77.02: 1.07
77 77.06:t:1.70
MUSE (Kim et al., 2024)
83.81
75.36:15.02
61.06:13.03
58.32:13.08
54.1443.23
52.14:3.49
31.07:4.58
35.66 35.67:14.68
DO2HSC (Zhang al., 2024)
88.83+6.58
86.80++6.21
77.12+-2.15
70.87+22.73
63.16++3.36
58.36+2..55
68.31 +-4.11
66.63++3.04
AGDiff
95,83-12.15
89.45:11.37
88.23310.67
84.06:0.59
77.59:3.39
68.15:11.9
1.821=1884
86.04:12.26
Table 2. Average AUCs and FI-Scores with standard deviation (10 trials) on four large-scale imbalanced graph datasets. The best results marked in bold, and "N/A" denotes the result is unavailable.
SW-620
MOLT-
PC-3
MCF-7
Method
AUC
FI-Score
AUC
Fl FI-Score
AUC
FI-Score
AUC
Fi-Score
OCGTI. (Qiu et al., 2022)
67.69+0.02
27.01 +0.90
57.42+2.38
53.38+0.64
68.42- 1.73
27.03++0.42
64.92+ 1.92
34.81 +1.70
GLocalKD (Ma al., 2022)
64.14=0.92
60.73+00.03
13,43+1.22
60.73+0.03
66.08-0.04
43.13++0114
61.43+1.20
45.00=0.17
iGAD (Zhang et al., 2022)
85.82.10.6
63.68.11.56
83,5911.077
63,30:11177
86.04_1.14
63.50:10.73
83.22.10.64
64.70.12.58
SIGNET (Liu el al., 2023a)
39.32.10.77
15.40
44.28.10.33
70.28110.16
40.56_3.05
76.17.10.31
40.22.1..55
68.30:10.42
MUSE (Kim et al., 2024)
N/A
N/A
N/A
N/A
49.18=2.42
76.60=t0.71
48.78=2.01
68.87=0099
DO2HSC (Zhang et al., 2024)
03.12
33.65:10.66
$1.51
1,.30:11.34
52.25=3.18
3..66::1.26
53.08-2..38
43.73::1.22
AGDiff
91.60
+.300
90.97+10.13
87.75 +.006
87.22+0.01
94.32-2.19
93.12++.83
89.38 0.86
87.25 0.39
standard deviations, which are computed over 10 indepen- dent runs of each algorithm to ensure reliable evaluation.
ing unsupervised, demonstrates competitive performance against iGAD. The superior performance of AGDiff can be attributed to the leverage of latent diffusion model, which generates pseudo-anomalous graphs to enrich the training process with diverse potential anomalous patterns. As a result, AGDiff can learn fine-grained distinctions between normal and anomalous graphs without relying on reconstruc- tion or labeled data, making it a robust and scalable solution for graph-level anomaly detection.
5.2. Comparison with State-of-the-arts Baselines
5.2.1. EXPERIMENT ON MODERATE-SCALE GLAD
Table presents the experimental results of AGDiff and other baseline methods moderate-scale graph datasets, where AGDiff consistently outperforms thte-o graph kernel and GNN-based GLAD methods across all datasets. For instance, on the DD dataset, AGDiff achieves a remarkable AUC of 88.23% and an Fl-score of 84.06%, significantly outperforming advanced baselines such as SIGNET (AUC: 70.67%, F1-Score: 59. 59.44%) MUSE (AUC: 61.06%, F1-Score: 58.32%), and DO2HSC (AUC: 66.04%, F1-Score: 61.14%). While graph kernel methods, such RW, show promising results on certain datasets, they usually suffer from scalability limitations, as seen with RW running out of memory on DD. Morcover, we can observe that the supervisd iGAD method generally achieves strong performance compared other baselines due to its access to partially labeled data. Nevertheless, AGDiff, despite be-
5.2.2. EXPERIMENT ON LARGE-SCALE IMBALANCED GLAD
Table 2 presents the experimental results of AGDiff and other baseline methods on large-scale imbalanced graph datasets. key observation from the results is the metric- specific strengths of certain baseline methods. For ex- ample, on SW-620, SIGNET achieves high F1-Score (75.40% (5540%) but low AUC (39.32%), while OCGTL achieves high AUC (67. (67.69%) but exhibits relatively low F1-Score (27. 01 ()). In contrast, we can observe that AGDiff con- sistently achieves superior performance on both metrics

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Leveraging Diffusion Model Pscudo-Anomalous Graph Generator for Graph-Level Anomaly Detection
0.2
0:35
100
Frequency Density
Normal Date
Frequency Density
horma Dats
80
F1.Score (%)
15
6225
AUC (%)
0.1
6:15
40
0.05
0.1
20
0:05
1e-4
1e-3 1e-21e-1
1el
1e2
1e3
Te-1
1e-3
1e-2 T6-1
1x1 1=2 163
Score
x10
Score
x10
(a) MUTAG
(a) ER MD
Preudo Apcentiue Dats
Anor nux Ears
80
F1-Score (%)
Freuuncy Danally
0.8
Data
Frequancy Densily
Date
(%)
60
0.6
0.3
20
101
10.41e33 1o-
1ef 1e2 1e3
0.2
0.4
0.6
0.8
0
0.2
0.4
0.5
0.0
(b) ER MD
Score
Score
(b) PC-3
Figure 3. Anomaly detection performance (AUC and FI-Score) on MUTAG and ER MD under different À values.
Figure 2. The scoring distribution of AGDiff on ER_MD and PC-3. The left and the right columns represent the results of the training stage and testing stage, respectively. Note that the r-axis and y-axis indicate the oulput scores and the number density of data samples within certain interval.
lies maintain structural similarities to normal graphs while introducing subtle deviations via the latent diffusion pro- cess. In contrast, real anomalous graphs are more distinctly separated from normal graphs, which implies that incorpo- rating pseudo-anomalous graphs during training improves the discriminative ability of the anomaly detector to iden- tify real anomalies. Moreover, in PC-3, we observe that the scoring distribution of pseudo-anomalous graphs pri- marily lies in low-score region, whereas real anomalous graphs remain well-separated from normal graphs in the test stage. This separation highlights the role of AGDiff in mod- eling the diversity of potential anomalies, which generates aheudo-graphe anomalies to provide rich anomalous signals to facilitate robust decision boundary learning, particularly in large-scale imbalanced scenarios.
across all datasets. Additionally, we observe that the semi- supervised method, iGAD, significantly outperforms other baselines (e.g., 86.04% AUC on PC-3) as it leverages partial real anomalies to refine its decision boundary. Nevertheless, AGDiff still surpasses iGAD despite being an unsupervised method across all datasets. For example, AGDiff achieves AUCs of 91.60% and 94.32% on SW-620 and PC-3, respec- tively, which improves by 5.78% and 8.28% over iGAD. The reason for this improvement is that although iGAD utilizes a certain amount of labeled anomalies to enhance the decision boundary learning. they may not be sufficiently representative of real anomalies due to the limited availabil- ity and diversity of anomalies in large-scale imbalance scenario. Different from semi-supervised iGAD, the di- verse pseudo-anomalous graphs generated from AGDiff pro- vide rich self-supervised signals for training. This enables the anomaly detector to distinguish between normal and anomalous graphs with subtle deviations. which effectively overcomes the limited diversity of available anomalies in imbalanced scenarios.
5.4. Parameter Analysis
To evaluate the impact of key hyper-parameters on the anomaly detection performance of AGDiff, we conduct sensitivity analysis on hyper-parameter X, which balances the contribution of the diffusion loss. Figure 3 shows the trend of AUC and F1-Score under different values of À on MUTAG and ER ER_MD. As shown in the figure, a moderate À generally improves performance as ensures AGDiff generates informative aseudo-anomaloon graphs, which in turn enhances the discriminative ability of the model. How- ever, excessively large À prioritizes diffusion modeling over classification, which tends to make the generated pseudo- anomalous graphs overly resemble normal graphs, thereby increasing the difficulty of training the anomaly detector. Conversely, a very small can also degrade the anomaly detection performance because limits the diversity of the generated pseudo anomalies.
5.3. Scoring Distribution Analysis
To verify the effectiveness of the secudo-anomalour graphs generated by AGDiff in facilitating anomaly detection, we analyze the scoring distributions of normal, pseudo- anomalous, and real anomalous graphs on the ER MD and PC-3 datasets, as shown in Figure In ER MD, pseudo- anomalous graphs exhibit a certain overlap with normal graphs, which indicates that generated geudo-graph anoma-
8

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Leveraging Diffusion Model Pscudo-Anomalous Graph Generator for Graph-Level Anomaly Detection
of anomalous data in graph-level anomaly detection. By introducing latent diffusion module inject controlled perturbations into graph representations, AGDiff is able to generate diverse apeudo-anomalooe graphs that closely re- semble normal ones while exhibiting subtle deviations. A GNN-based anomaly detector is then jointly trained with the latent diffusion module to distinguish the pseudo-anomalous and normal graphs. Moreover, we theoretically demon- strated the effectiveness of these perturbed graphs generated via AGDiff for facilitating the learning of more robust decision boundary. Empirical evaluations on multiple graph benchmarks validate the superiority of AGDiff against state- of- GLAD baselines. Two limitations of this work are: (1) It assumes a sufficiently representative distribution of normal graphs, which may not hold in shifting or highly het- erogeneous environments. (2) While AGDiff can generate pseudo graph anomalies to enhance decision boundary train- ing, it is currently limited to static graphs. Future research can focus on exploring more flexible noise scheduling dif- fusion approaches, as well as investigating the challenging GLAD tasks in heterogencous environments or dynamic graph settings.
Table Ablation study results on MUTAG and FR_MD.
MUTAG
ER MD
Method
AUC
Fi-Score
AUC
FI-Soore
w/o Pre-train
21.764-26.6
72/224-2721
64. 10:-9.87
61.49:9.54
w/o Condition
63.624:38.32
65.19:37.44
68.40:0.21
65.19:0.60
w/o Latent Diffusion
48.16-4.46
50.67+11.99
63,88
58.48+ 1.54
AGDiff
95.83.2..15
89.45
91.21:11844
26.04
5.5. Ablation Study
We conduct an ablation study to analyze the impact of each component in AGDiff, including the pre-training strategy, condition embedding, and the latent diffusion module. Par- ticularly, we utilize the reconstruction error to detect anoma- lies when we remove the conditioned latent diffusion mod- ule, as pseudo-anomalous graphs are not available in this variant. Table 3 presents the experimental results on MU- TAG and ER_MD, where we can have the following ob- servations. First, the significant performance degradation when the pertaining strategy indicates the importance of pre- training to our framework, as it provides well-structured latent space for modeling the normality, so that the model is able to generate informative pseudo-anomalous graphs. Sec- ond, we can observe that removing the condition embedding also significantly degrades the anomaly detection perfor- mance. This is because the condition embedding injects additional variability via introducing a noise-augmented condition vector, which encourages the model to generate diverse pseudo-anomalous samples that better capture the nuances of anomalous patterns. Otherwise, the generated graphs may closely resemble normal graphs, which leads to the difficulty of distinguishing them. Lastly, we observe the most severe performance decline in the reconstruction based variants, which highlights the limitations of reconstruction- based methods, which generally struggle to differentiate between normal and anomalous graphs when structural de- viations are subtle. In contrast, our approach leverages the la- tent diffusion process to explicitly model pseudo-anomalos variations, providing more robust and discriminative learn- ing signals for training the anomaly detector.
A Acknowledgement
This research is supported by the National Research Foun- dation Singapore and DSO National Laboratories under the AI Singapore Programme (AISG Award No: AISG2-RP- 2020-018).
Impact Statement
This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here.
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Leveraging Diffusion Model Pscudo-Anomalous Graph Generator for Graph-Level Anomaly Detection
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Leveraging Diffusion Model Pscudo-Anomalous Graph Generator for Graph-Level Anomaly Detection
A. Algorithm Analysis
Theoretical Analysis. Here we introduce two algorithms to achieve anomaly detection when given normal data. Specif- ically, when given a normal dataset Grommal the algorithm A, first generates a number of normal data Gen(Gnomma) with some generation method Gen(-) (e.g. diffusion process) by the given normal data Gmoemal then whether new dataset is anomalous is determined by the data divergence d(g, ) If d(G, g > ddGGen (G Gnommal) then G is classified as anomalous data. For the algorithm A2, it first perturbs the normal dataset Guonnal to get perturbed dataset Gnormal then use the same generation method Gen(-) to generate a number of perturbed data Gen(g ). This generated perturbed data is regarded as auxiliary anomalous data, and finally A2 uses a classifier to obtain a decision boundary for Guormal and Gen ) The criterion for A2 becomes that if d(g.guoma)) > d(G, Gen (Gnormal)) )) then G is classified as anomalous data.
Notice that it is reasonable assume under the same generation method Gen(-), the reconstruction error between the original data and the generated data does not change, i.e., d d(Gen(Guomma) Guormal) = dl (Goornll Gen )) Therefore,
m G)omma))))) d(g) Gen Gen(Gromal)) Ghomml)).
then once A1 successfully detects the anomalous data, Ag can also successfully detect the anomalous data, which implies that A2 is better than A in detecting the anomalous data.
Reconstruction Error
1.0
40-
W
F1-Score (%)
40
0.6
AUC
20
0.4
10
10-
0.2-
-10
10-
100
100
80
100
Epoch
Epoch
Epoch
(a) Test Reconstruction Error
(b) AUC (A2)) AUC
(c) F1-Score (A2z) F1 -Score (AA2)
Figure 4. Empirical study results, including the reconstruction error trends and performance gap (both AUC and F1-Score) between Ai and A on ER MD dataset.
Empirical Analysis. We empirically validate our theoretical analysis through comprehensive experiments on the ER_MD dataset, examining both reconstruction error dynamics and anomaly detection performance over 100 training epochs. Our evaluation metrics include reconstruction error, AUC, and F1-Score the test set. Figure 4 presents the results of the test set across training epochs for Ai and A2, where have the following key observations:
The reconstruction error of A1 decreases in the early training stages while gradually increasing afterward. This trend suggests overfitting to normal data, where Ai effectively learns to reconstruct normal graphs, leading to sharp reduction in reconstruction error. This pattern indicates that while A₁ effectively learns to reconstruct normal graphs in early stages, it subsequently overfits the training distribution, compromising its generalization capability unseen test data, which can be observed in the performance gap changes in AUC and F1-Score.
A2 consistently exhibits a higher and fluctuating reconstruction error throughout training. This observation suggests that the introduction uscudo-anomalout graphs prevents overfitting to normal patterns, which makes the model Iearn a more discriminative representation. Unlike Ar which primarily minimizes reconstruction loss, Ag actively differentiates between normal and anomalous graphs, as reflected in the AUC gap: while initially lagging behind A1. A steadily improves and eventually surpasses Ai as its classifier learns leverage pseudo-anomalous data for decision boundary refinement.
Since anomalous graphs inherently exhibit higher reconstruction errors, an effective anomaly detection model should maintain sufficient error gap between normal and abnormal samples. This is validated by the AUC trends, where A eventually surpasses A1, demonstrating that its classifier progressively refines decision boundary by effectively
13

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Leveraging Diffusion Model Pscudo-Anomalous Graph Generator for Graph-Level Anomaly Detection
incorporating pseudo-anomalous graphs. The stabilization of the AUC gap in later epochs suggests that Ag converges to robust and generalizable anomaly detection model, whereas A remains constrained by its reliance reconstruction.
These empirical results validate our theoretical analysis that as the reconstruction error increases, our method becomes more robust. Specifically, when the reconstruction error small, both Ai and A₂ achieve similar anomaly detection performance. While the reconstruction error increases, A2 significantly outperforms A1, which matches our theoretical results that decision boundary learning via pseudo-anomalous graphs leads superior anomaly detection. Compared to the purely reconstruction based strategy of A1, the explicit optimization of decision boundaries through anoomloos graphs in A2 offers a more robust solution for graph-level anomaly detection.
B. Datasets
Table 4 presents the details of the graph datasets used in our experiments, including the number of graphs, average nodes, average edges, node classes, and graph classes. Additionally, we also provide the anomaly ratio and data type of each dataset in the table.
Table 4. Detailed information of the graph benchmark datasets.
Datasct Name
# Graphs
# Average
[V]
Average
[F]
Node Classes
Graph Classes
Anomalous Rate
Data Types
MUTAG
188
17.93
19.79
2
33.51%
Molecule
COX2
467
41.22
43.45
2
21.84%
Molecule
ER_MD
446
21.33
234.85
10
2
40.58%
Molecule
1,178
284.32
715.66
41.34%
Biology
SW-620
40,532
26.06
28.09
65
2
5.95%
Molecule
MOLT-4
39,765
26.10
28.14
7.90%
Molecule
PC-3
27,509
26.36
28.49
45
2
9.34%
Molecule
MCF-7
27,770
26.40
28.53
8.26%
Molecule
C. Implementation Details
Here we provide the implementation details in our experiment, including the data split, network architecture, hyper-parameter setting, baseline setting, and computing resources follows:
Data Split: For small to moderate-scale datasets, we follow the data split method used in (Zhang et al., 2024). Specifically, 80% the normal data used for training, while the test set combines remaining normal samples with an equal or smaller number of anomalies. For large-scale imbalanced datasets, 80% of the normal data is allocated for training, and the test set includes the rest of the normal data along with all anomalies.
Network Architecture: Following prior works (Ma et al., 2022; Zhang et al., 2024), we adopt the Graph Isomorphism Network (GIN) (Xu et al., 2019) as the backbone. Both the pre-trained graph representation learning model and the anomaly detector are constructed with 3 GIN layers. Additionally, we employ 2-layer MLP for both the perturbation condition model and the projector within the anomaly detector. The latent dimension is set to 16 for moderate-scale datasets and 512 for large-scale datasets.
Hyper-parameter Setting: We adopt Adam (Kingma & Ba, 2014) optimizer with fixed learning rate p = 0.001 for both pre-training and training stages. We first pre-train the graph generator for 100 epochs, with the KL-divergence loss coefficient set 0.001. The diffusion process employs a fixed time step of 1, 000 for all datasets. In training, we adopt batch size of 16 for moderate-scale datasets and 512 for large-scale datasets. The full model is trained for 200 epochs. To balance the contribution of the diffusion loss, tune the coefficient À via grid search over the range [0.0001, 1000] to achieve optimal performance. We also evaluate the impact of À in Section 5.4.
We access the official codes of all graph kernel methods from the GraKel repository (Siglidis et al., 2020), where we extract the kernel matrix on each dataset and apply OCSVM (via Scikit-learn (Pedregosa et al., 201 1)) to achieve anomaly detection. For the GNN-based GLAD baselines, we reproduce all the results of the compared method by reproducing their officially released codes. Particularly, we employ the same architecture of the backbone network and the data split strategy as the proposed AGDiff ensure fair comparison.
Baseline Setting:
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Leveraging Diffusion Model Pscudo-Anomalous Graph Generator for Graph-Level Anomaly Detection
x10
.10
110
10-
5-
0-
22
X10
-5
-15
x10'
X10
x10
X10"
0.5
1.5
x16
(a) OCGTL (SC-0.07)
(b) GLocalKD (SC-0.13)
(c) SIGNET (SC=0.01)
x160
x0
X10
0-
-5-
-1-
-3
-10
-2
x10
x10
x102 X
110P
x10'2
(d) MUSE (SC=0.14)
(c) DOZHSC (SC=0.08)
(f) AGDiff (SC=0.61)
Figure 5. The t-SNE visualization comparison on ER. MD dataset, where the data points marked in purple, blue, and red represent training normal graphs, testing normal graphs and anomalous graphs, respectively. SC denotes the Silhouette Coefficient metric, which is used for evaluating.
Computing Resources: All the experiments in this paper are performed on the NVIDIA Tesla H100 GPU (80GB) with Intel Xeon Platinum 8480CL CPU.
D. Visualization Results
To analyze how different methods capture graph representations, we employ t-SNE (Van der Maaten & Hinton, 2008) to visualize the latent embeddings of AGDiff and several baseline methods for comparison. As shown in Figure 5, we can observe that the latent embeddings of AGDiff exhibit a more compact and well-separated structure, with normal and anomalous graphs forming distinct regions in the latent space. This observation suggests that our model effectively simulates subtle deviations from normality. Moreover, to quantitatively evaluate the effectiveness of the Iearned representations in AGDiff, we further calculate the Silhouette Score (SC) between normal and anomalous embeddings for each method. Note that the value of SC ranges from [-1, and a higher SC indicates a better separation. From this table, we can observe that AGDiff achieves an SC of 0.61, which is significantly higher than state-of-the-art GLAD baselines such as MUSE (SC- = 0.14), DO2HSC (SC = 0.08), and SIGNET (SC = 0.01). This observation indicates a better separation between normal and anomalous embeddings from statistical perspective. These results highlight the effectiveness of our approach in learning expressive and anomaly-aware graph representations for anomaly detection.
In order to more intuitively understanding the generated pseudo graphs, we randomly pick four pairs of generated pscudo graphs and normal graphs to visualize their graph structures, as shown in Figure 6. These pseudo graphs exhibit noticeable structural deviations from their normal counterparts, such as the varied density and sparser connections in different regions, and modified local connectivity patterns around nodes. For example, some generated graphs exhibit sparser regions or more peripheral nodes (e.g., the first and fourth pseudo graphs the second row). These visual discrepancies are critical as they empirically validate the rationale of these generated pseudo graph anomalies in helping train the anomaly detector. In particular, we further utilize the normalized Laplacian spectral distance to quantify the discrepancy between the generated anomalies and normal graphs. Specifically, we computed pair- wair-wise spectral discrepancies between: (1) Generated pseudo- anomalous graphs and normal graphs, which ranged in 10, 1.12]. and (2) Real anomalous graphs and normal graphs, which ranged in [0.40 40, 5.12]. And the corresponding Laplacian spectral distances of the examples in Figure 6 are larger than the minimum pair-wise discrepancy of real anomalies. While the range for pseudo anomalies is narrower compared to real anomalies, this outcome aligns with our design intent. Rather than mimicking the extreme deviations observed in real anomalies, we aimed to produce controlled yet challenging perturbations to enhance the decision boundary learning. These
15

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Leveraging Diffusion Model Pseudo-Anomalous Graph Generator for Graph-Level Anomaly Detection
(a) Original Nomal Graph
(b) Generated Pscudo Graph
Figure 6. The visual comparison of normal and generated pseudo graphs pairs the ER MD dataset. Note that the normalized Laplacian spectral distances between each pair this figure are 0.44, 0.43, 0.62, 0.43, respectively.
results indicate that the generated pseudo anomalies exhibit meaningful discrepancy from the normal graphs, providing sufficient diversity to effectively challenge the model during training.
E. More Parameter Analysis
Effect of Different Noise Magnitudes 7/. To evaluate the effect of the noise magnitude parameter 1) on the performance of AGDiff, conduct an experiment by varying from wide range [0, 100). Table 5 presents the experimental results. We observe performance degradation when this noise term is removed (i.e., 17 0) or set to excessive value (e.g., 77 10). Our explanation for these observations is that (1) removing the noise term may lead to over-proximity between the pseudo graph anomalies and the normal graph, thus making it difficult to train an anomaly detector. (2) While an excessively
high y can lead to pseudo anomalies that deviate too far from normal data, thus reducing the discriminative ability of the anomaly detector. These findings highlight the importance of balancing 7) to ensure meaningful perturbation to the initial latent representation.
Table Anomaly detection performance of different noise magnitudes r on MUTAG and ER.MD
The best results are marked bold.
Datasets
Metrics
r) =
1) = 0.01
1) = 0.1
1=
" = 10
100
AUC
93.20+2264
92.64+0.32
92.40=0.088
95.83+:2.15
92.00110.00
92.00=10.00
MUTAG F1-Score
86.00-+2.00
88.00+00.00
88.00+00.00
49.45+11.77
88.00-F0.00
88.00++0.00
AUC
82.95-12.17
86.81+0.91
87.78+1.07
91.21+11.4
82.08-10.52
81.76++0.59
MD
F1-Score
7..36=1.89
80.19+2.83
85.09+0.94
86.04+2.26
71.70+00.00
72.64
Effect of Different Time Steps T in Diffusion Sampling. Here we also analyze the performance fluctuations when setting different time steps T on the MUTAG and ER MD datasets. It can be observed that the performance (e.g., on MUTAG) generally improves from T 250 (91.52% AUC) to T = 750 (95.84% AUC) or = 1000 (95.83% AUC), with performance platcauing or slightly declining when T 2 1000. A trend was similarly observed on ER.MD which indicates that a low may insufficient to generate high-quality pseudo graphs. Nevertheless, a high can also lead
16

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Leveraging Diffusion Model Pseudo-Anomalous Graph Generator for Graph-Level Anomaly Detection
over-diffusion, making the generated graphs excessively similar to normal graphs, which in rurn diminishes the capability of the anomaly detector to differentiate them and increases computational cost well. These findings highlight the importance of appropriately selecting T to balance the generation quality and computational cost.
Table 6. Anomaly detection performance (AUCs and Fl-Scores) of different time steps T on MUTAG and ER_MD in diffusion sampling process. The best results are marked bold.
Datasets
Metrics
T = 250 T 500
T 750
T = 1000
T 1250
T = 1500
AUC
91.52+77.84
95.20=#3.20
95.84:13.84
95.83++2.15
92.00=10.00
92.00=00.00
MUTAG
F1-Score
88.00-14.00
92.00=+0.00
94.00-1-..0
89.45-+1.37
87.00
87.00++0.00
AUC
86.61+4.38
89.30++0.3
84.48+22.17
91.21+11.84
82.34++.113
82.18
MR
Fl-Score
78.30:16.60
83.02::1.89
79.25:1.66
86.04
73.58
73.58
F. Ablation Study on the Number of Generated Graphs
In our initial experimental design, we set the number of generated pseudo-anomalous graphs equal to the number normal graphs. This choice was based on the rationale that a balanced data configuration would likely foster more stable training dynamics and prevent the model from being biased towards the normal class. Here, further conduct ablation study on the anomaly ratio which represents the proportion of generated pseudo graphs relative the quantity of normal graphs available in the training set. Table 7 shows the experimental results on the DD dataset, which offers key insight into our anomaly detection framework under an imbalanced setting (Fang et al., 2025). The results show that a balanced data composition (i.e., r = 100%) is crucial for robust learning and yields the best performance. In addition, the observed trend, where performance (AUC) and stability (represented by the standard deviation) are improved from 85.06 = 3.42 (r 30%) 88.23 + 0.67 (r 100%). This implies that the effective learning of the anomaly boundary heavily relies on the richness and sufficiency of the pseudo-anomalous graphs. Insufficiently generated graphs (e.g., r 60%) appear to create an "information bottleneck", which limits the ability of the model to generalize the concept of anomaly from an undersampled and less diverse space.
Table 7. Anomaly detection performance under different anomaly ratios r. The best results are marked in bold.
Dataset
Metrics
r' 30%
r r= -0%
-= 90%
r -= 100%
AUC
85.0613.42
86.72=1.70
87.30=10.49
88.23110667
DD
F1-Score
80.78+44.48
83.23
84.03++0.36
8.59
17


Reviews:
[{"review_id": "ISmlfThGdb", "reviewer": "Reviewer_PZBE", "summary": "The paper introduces a graph-level anomaly detection method to improve the performance of GNNs on anomalous graphs. The method consists in generating pseudo-anomalous graph with diffusion models in other to enhance the classification capabilities.", "questions": "", "limitations": "", "rating": 3, "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": "**We thank the reviewer for the comments. Hope our responses below help to solve your concerns.**\n\n**To Q1:**\n1. **What are pseudo-anomalous graphs?** Pseudo-anomalous graphs are graphs generated via a controlled latent diffusion process (refer to Section 4.3). These graphs are optimized to resemble normal graphs yet exhibit subtle deviations, therefore mimicking potential anomalies and providing effective auxiliary signals for refining the decision boundary.\n2. **Why are they pseudo-anomalous and not simply anomalous?** The graphs are termed \"pseudo-anomalous\" as they are not sampled from real anomaly data, but are generated by introducing subtle perturbations to normal graphs. In unsupervised GLAD, real anomalous data is not utilized during training. Therefore, our approach leverages pseudo-anomalous graphs to compensate for this absence.\n\n**To Q2:** Please note that our work focuses on GLAD, and is not merely a data augmentation paper. We want to highlight two key innovations of AGDiff beyond standard augmentation:\n1. AGDiff leverages a conditioned latent diffusion process to generate pseudo-anomalous graphs from normal data (Section 4.3), which is not arbitrary augmentation but a targeted approach to simulate potential graph-level anomalies via controlled perturbation in an unsupervised manner, which addresses the anomaly scarcity problem in GLAD. Therefore, our approach is distinctly different from GOEM [Liu et al.]’s supervised diffusion process (relying on labeled anomalies) and CAGAD [Xiao et al.]’s counterfactual augmentation (based on modifying the neighboring node attributes).\n2. Unlike the traditional augmentation paradigm where augmentation is decoupled from learning, AGDiff integrates the diffusion process and anomaly detection in a joint training framework (Section 4.4). This enables bidirectional feedback where the detector refines the generation process, and the generator is adapted based on feedback from the detector to generate more challenging pseudo-anomaly samples.\n\nMoreover, we want to emphasize that GOEM [Liu et al.] and CAGAD [Xiao et al.] are designed for node-level tasks, which differs fundamentally from AGDiff. Our approach is specifically tailored for graph-level anomaly detection, addressing the scarcity of anomalous data with an unsupervised and adaptive strategy.\n\n**To Q3:** The positive effect of the pseudo-anomalous data can be validated in the following parts of our paper: (1) In the ablation study (Table 3), the performance significantly drops ($\\geq$ 20\\%) when we remove the latent diffusion module (no pseudo-anomalous data generated) or the conditioned vector (determine the generation quality of pseudo-anomalous data). (2) Refer to Appendix A - through the theoretical analysis and empirical comparison with the reconstruction-based model, we demonstrated the benefits of pseudo-anomalous data in improving the discrimination capability of the anomaly detector. These findings are good evidence of the contribution of pseudo-anomalous data.\n\n**To Q: Theoretical Claims:** We theoretically and empirically demonstrated why AGDiff could outperform the reconstructor-based approach. (Refer to comments of Reviewer kMMx, BUES, and 2Zh2)\n\n**To Q: Experimental Designs Or Analyses:** Here are the summarized questions that our experiments answered:\n```\n1. How does AGDiff compare with SOTA GLAD baselines? (Refer to Table 1)\n2. How does AGDiff perform in large-scale imbalanced GLAD? (Refer to Table 2)\n3. How can AGDiff's discrimination ability be verified? (Refer to Figures 2 & 5)\n4. How does the hyper-parameter impact the performance? (Refer to Figure 3)\n5. How does each component in AGDiff contribute to performance? (Refer to Table 3)\n6. Why can AGDiff outperform reconstruction-based methods? (Refer to Appendix A)\n```\nWe have further answered several questions in the rebuttal (see responses to Reviewers kMMx's W2\\&W4, BUES's W2\\&W4, 2Zh2's W3). If you have other questions, please feel free to discuss them with us.\n\n**To Q: Supplementary Material:**\n1. We set the number of generated graphs equal to the normal graphs as this balanced configuration leads to more stable training. As per your suggestion, we further conducted an ablation study by varying the ratio $r$ of generated pseudo graphs relative to normal graphs. The results (on DD) below indicate that the balanced setting (i.e., 100\\% ratio) yields the best performance.\n\n$\\begin{matrix}\n\\\\hline\n&\\text{Metrics}&r=30\\\\%&r=60\\\\%&r=90\\\\%&r=100\\\\%\\\\\\\\\\hline\n\\text{DD}&\\text{AUC}&85.06(3.42)&86.72(0.70)&87.30(0.49)&\\bf88.23(0.67)\\\\\\\\\n&\\text{F1-Score}&80.78(4.48)&83.23(1.45)&84.03(0.36)&\\bf84.06(0.59)\\\\\\\\\\hline\n\\end{matrix}$\n\n2. It is important to clarify that we are not training the GNN using the diffusion model. The diffusion model is jointly trained with the anomaly detector (GNN as the backbone), and functions as a perturbator to generate pseudo-anomalous graphs. We have analyzed AGDiff's time complexity (refer to Reviewer BUES's W2).", "claims_and_evidence": "The paper claims to that generating pseudo-anamalous graphs improves the learning capabilities of GNNs.", "methods_and_evaluation_criteria": "The paper fails to verify the claim that it puts forward. \n\n1. What are pseudo-anomalous graphs? Why are they pseudo-anomalous and not simply anomalous? \n2. This method is simply data augmentation utilizing a generative model. What is the novelty of the method beyond putting two existing pieces together? \n3. There is no proof that the improvement of the method is actually because of the pseudo-anomalous data. By are the authors claiming this? How do they verify this?", "theoretical_claims": "The authors do not put any theoretical claims forward.", "experimental_designs_or_analyses": "I believe the experimental design does not help in answering the questions.", "relation_to_broader_scientific_literature": "I believe the paper is a data augmentation paper. \n\nData Augmentation for Supervised Graph Outlier Detection via Latent Diffusion Models\nKay Liu, Hengrui Zhang, Ziqing Hu, Fangxin Wang, Philip S. Yu\n\nCounterfactual Data Augmentation With Denoising\nDiffusion for Graph Anomaly Detection\nXiao et al.", "essential_references_not_discussed": "See item before.", "other_strengths_and_weaknesses": "I believe the paper has very little novelty.", "other_comments_or_suggestions": "None.", "questions_for_authors": "See before.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "l29Z4rApxJ", "reviewer": "Reviewer_kMMx", "summary": "This paper introduces Anomalous Graph Diffusion (AGDiff), a novel graph-level anomaly detection (GLAD) framework that consists of three core components: (1) a pre-training module employing variational inference to learn a structured latent space, (2) a latent diffusion process that introduces controlled perturbations to generate pseudo-anomalous graphs, and (3) a jointly trained graph anomaly detector that distinguishes normal graphs from pseudo-anomalous graphs. The central idea is to mitigate the scarcity of anomalous graphs in GLAD by generating diverse pseudo graph anomalies through a perturbation conditioned latent diffusion process. Experimental results demonstrate that AGDiff significantly outperforms state-of-the-art GLAD baselines on diverse GLAD tasks.", "questions": "", "limitations": "", "rating": 4, "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": "**We thank the reviewer for the comments. Hope our responses below are helpful in solving your concerns.**\n\n**To W1:** The KL divergence term in Eq. 7 is crucial for regularizing the latent space during pre-training. By encouraging the latent distribution $\\mathbf{Z}$ to align with the standard normal prior $\\mathcal{N}(\\mathbf{0}, \\mathbf{I})$, it prevents the model from overfitting to a narrow or degenerate latent manifold [1]. This well-structured latent space is key for generating diverse pseudo-anomalous graphs in subsequent stages. We will highlight this in our paper.\n\n```\n[1] Kipf, Thomas N., and Max Welling. Variational Graph Auto-Encoders, NeurIPS Workshop on Bayesian Deep Learning, 2016.\n```\n\n**To W2:** We have tested the effect of different noise magnitudes $\\eta$ on MUTAG and ER\\_MD, as summarized in the table below.\n\n$\\begin{matrix}\n\\\\hline\n\\text{Datasets}&\\text{Metrics}&\\eta=0&\\eta=0.01&\\eta=0.1&\\eta=1&\\eta=10&\\eta=100\\\\\\\\\\\\hline\n\\text{MUTAG}&\\text{AUC}&93.20(2.64)&92.64(0.32)&92.40(0.08)&\\bf95.83(2.15)&92.00(0.00)&92.00(0.00)\\\\\\\\\n&\\text{F1-Score}&86.00(2.00)&88.00(0.00)& 88.00(0.00)&\\\\bf89.45(1.37)& 88.00(0.00)& 88.00(0.00)\\\\\\\\\\\\hline\n\\text{ER\\\\_MD}&\\text{AUC}&82.95(2.17)&86.81(0.91)&87.78(1.07)&\\\\bf91.21(1.84)&82.08(0.52)&81.76(0.59)\\\\\\\\\n&\\text{F1-Score}&77.36(1.89)&80.19(2.83)&85.09(0.94)&\\\\bf86.04(2.26)&71.70(0.00)&72.64(0.94)\\\\\\\\\\\\hline\n\\end{matrix}$\n    \nWe can observe a performance degradation when this noise term is removed (i.e., $\\eta=0$) or set to an excessive value (e.g., $\\eta=10$). Our explanation for these observations is that (1) removing the noise term may lead to over-proximity between the pseudo graph anomalies and the normal graph, thus making it difficult to train an anomaly detector. (2) While an excessively high $\\eta$ can lead to pseudo anomalies that deviate too far from normal data, thus reducing the discriminative ability of the anomaly detector. These findings highlight the importance of balancing $\\eta$ to ensure meaningful perturbation to the initial latent representation $\\mathbf{Z}_{0}$.\n\n**To W3:** We have added a visualization comparing pseudo anomalies with normal graphs, available at https://anonymous.4open.science/r/AGDiff-137F/visualization/ (under the \"visualization\" file). The visualization results clearly illustrate that while the pseudo anomalies lie close to the normal data (with certain overlaps), they consistently exhibit subtle deviations, which serves as good evidence to support our claim. We will include these visual comparisons in the paper.\n\n**To W4:** First, we have performed a quantitative analysis of the diversity of pseudo-anomalous graphs on ER\\_MD. Except for that, rather than graph edit distance (which has $\\mathcal{O}(n^{3})$ complexity), we employed the **normalized Laplacian spectral distance** to measure the discrepancy between the generated anomalies and normal graphs, as it is computationally efficient and direct related to graph topology. Specifically, we computed pair-wise spectral discrepancies between:  \n1. **Generated pseudo-anomalous graphs and normal graphs**, which ranged in $[0.17, 1.12]$.\n2. **Real anomalous graphs and normal graphs**, which ranged in $[0.40, 5.12]$.\n\nWhile the range for pseudo anomalies is narrower compared to real anomalies, this outcome aligns with our design intent. Rather than mimicking the extreme deviations observed in real anomalies, we aimed to produce controlled yet challenging perturbations to enhance the decision boundary learning. The embedding visualization results (in our response to W3) further support this, where the pseudo anomalies are distinctly separable from normal graphs. These results indicate that the generated pseudo anomalies exhibit a meaningful discrepancy from the normal graphs, providing sufficient diversity to effectively challenge the model during training.", "claims_and_evidence": "The advantages of AGDiff over other GLAD baselines have been validated via extensive experiments. However, the claim that the generated pseudo-anomalies of AGDiff \"closely resemble normal graphs\" is only qualitatively discussed via t-SNE visualizations (Appendix D). A quantitative analysis with similarity metrics, e.g., graph edit distance between generated and normal graphs would strengthen this claim.", "methods_and_evaluation_criteria": "The proposed method makes sense for the GLAD problem. The evaluation metrics (AUC and F1-Score) are standard for GLAD, and the benchmark datasets cover both moderate-scale and large-scale imbalanced scenarios, which make sense for real-world GLAD problem.", "theoretical_claims": "I have checked the theoretical analysis of this paper in the appendix, where AGDiff (Algorithm $\\mathcal{A}\\_{2}$) is compared with reconstruction-based model (Algorithm $\\mathcal{A}\\_{1}$), and the related analysis is compelling.", "experimental_designs_or_analyses": "I have checked the soundness of experimental designs and analyses of this paper. The experimental design (Tables 1 and 2) is sound and reliable, which employs consistent data splits and fair baseline comparisons.", "relation_to_broader_scientific_literature": "Different from the diffusion model-based AD approaches [1, 2] that focus on modeling data normality, AGDiff proposes to leverage the diffusion model as the perturbator for normal data, which provides a novel and promising solution for addressing the anomaly scarcity challenge and make it distinct from supervised GLAD approaches reliant on labeled data. \n\n[1] Diffusion models for medical anomaly detection. MICCAI, 2022\n\n[2] Dynamic addition of noise in a diffusion model for anomaly detection. CVPR, 2024", "essential_references_not_discussed": "The literature review is thorough, with key related works appropriately cited.", "other_strengths_and_weaknesses": "**Strengths:**\n1. The proposed AGDiff method tackles the challenge of anomaly scarcity in GLAD by generating pseudo-anomalous graphs via a latent diffusion process, which surpasses existing GLAD methods and shows significant novelty and promising potential impact.\n2. The theoretical analysis in appendix A well supports the validity of the proposed method, which provides empirical trends in both reconstruction errors and performance metrics to demonstrate that the generated pseudo-anomalous graphs enhance the decision boundary learning.\n3. AGDiff achieves state-of-the-art performance compared to existing GLAD approaches on diverse benchmark datasets, particularly in imbalanced settings. The ablation study also validates the importance of each component. The experimental results reflects the practical effectiveness and adaptability of the proposed method.\n\n**Weaknesses:**\n1. The effect of the KL divergence term (Eq. 7) in the pre-training phase requires clarification. Can the authors further explain it?\n2. Eq. 10 introduces noise $\\eta$ to perturb latent embeddings, while its influence on anomaly detection performance is not discussed.\n3. While the empirical results show that the generated pseudo graph anomalies improve anomaly detection, the authors are encouraged to provide some visual comparisons between the generated pseudo anomalies and normal graphs, which would improve the interpretability of the proposed method. \n4. This paper refers to the “diversity” of the generated pseudo graph anomalies, but only qualitatively through the t-SNE visualization. Are there quantitative metrics, e.g., graph edit distance or MMD, to assess the discrepancy of the generated samples compared to normal graphs?", "other_comments_or_suggestions": "I have no other comments or suggestions for this paper.", "questions_for_authors": "Please refer to Weaknesses above.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "vQkIxMC37t", "reviewer": "Reviewer_BUES", "summary": "This paper presents a diffusion-based method for generating pseudo-anomalous graphs to address anomaly scarcity in GLAD. It employs a latent diffusion process with perturbation conditions and a joint training scheme for anomaly detection. Experiments on both balanced and imbalanced datasets demonstrate its effectiveness.", "questions": "", "limitations": "", "rating": 4, "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": "**Thank you for your recognition, and we hope the responses below can solve your concerns:**\n\n**To W1:** AGDiff ensures the gap between normal and pseudo-anomalous graphs via its **controlled latent diffusion process** and **joint training**. Rather than using arbitrary noise, the conditioned vector (Eq. 10) introduces learnable perturbations that simulate potential and diverse anomalous patterns while preserving structural plausibility. There are several pieces of evidence to support this claim, e.g., (1) Varying $\\eta$ influences the generation quality of pseudo graph anomalies, thereby influencing the final performance (refer to Reviewer kMMx's W2). (2) Removing the conditioning vector $\\mathbf{c}$ leads to a substantial performance drop (refer to  Reviewer 2Zh2's W1). (3) Our statistical analysis (refer to  Reviewer kMMx's W4) confirms that there is indeed a meaningful gap between pseudo-anomalous graphs and normal graphs.\n\n**To W2:** Here, we provide a computational complexity analysis for AGDiff. For a dataset of $N$ graphs, each with an average of $m$ nodes (feature dimension $d$), $|E|$ edges, and latent dimension $d_{z}$, the AGDiff framework operates in three phases:\n\n1. **Pre-training:** An $L$-layer GIN is employed as the backbone network in the pre-training, where the overall complexity is $\\mathcal{O}(N L (|E|d + m d^{2}))$ due to the message aggregation ($\\mathcal{O}(|E|d)$) and feature transformation ($\\mathcal{O}(m d^{2})$).\n2. **Pseudo Anomaly Generation:** This phase involves the computation of conditional vector ($\\mathcal{O}(N d_{z}^{2})$) and a $T$-step latent diffusion process ($\\mathcal{O}(N T m d_{z}^{2})$) across all graphs.\n3. **Decoding \\& Anomaly Detection:** Decoding involves the computation of node attributes and adjacency matrices from latent embeddings, which results in time complexity of $\\mathcal{O}(N|E|d_{z})$ when we apply a negative sampling strategy in practice. The computational complexity of the anomaly detector is similar to the pre-training stage, i.e., ($\\mathcal{O}(N L(|E|d + m d^{2}))$), due to their similar network structure.\n\nTherefore, the overall computational complexity of AGDiff is approximately $\\mathcal{O}(N L (|E|d + m d^{2}) + N (T m+1) d_{z}^{2} + N|E|d_{z})$, which is comparable with other state-of-the-art baselines such as SIGNET, MUSE, DO2HSC. Besides, potential optimizations like using parallel computation further enhance efficiency. We will add this analysis to the paper.\n\n**To W3:** We would like to address your concern from two perspectives:\n1. **Subtle Deviations Facilitate Decision Boundary Learning.**  In $\\mathcal{A}_{2}$, perturbing normal data before the generation process aims to ensure subtle deviations of the generated pseudo-anomalous graphs from normal graphs, which is critical for effective decision boundary learning. Relevant evidence can be found in the response to Reviewer kMMx’s W2.\n\n2. **Learnable Perturbations Expand Anomaly Diversity.** Directly using perturbed normal data as pseudo anomalies would constrain the diversity of anomalous patterns the model encounters, as the perturbations would be static and lack adaptability. This limitation may cause the overfitting of the classifier to a narrow set of pseudo anomalies, reducing its generalizability. In $\\mathcal{A}_2$, however, the perturbations are learnable and dynamically adjusted during joint training with the anomaly detector. As the detector improves, the perturbation mechanism evolves, generating increasingly sophisticated and varied pseudo anomalies. This adaptive process exposes the model to a broader spectrum of potential anomalies, enhancing its robustness and generalization.\n\n**To W4:** We have provided the implementation code of AGDiff at https://anonymous.4open.science/r/AGDiff-137F/. The link is fully anonymous, and some pre-trained models are also attached for reproducibility.\n \n**To Other Comments:** We will double-check our paper and correct all identified grammatical and formatting issues such as replacing \"Let … denotes\" with \"Let … denote\".", "claims_and_evidence": "Yes, the manuscript claims that the proposed method, which integrates an innovatively designed latent diffusion model as a perturbator to generate pseudo-anomalous graphs, outperforms reconstruction error-based approaches by leveraging these generated graphs to refine the decision boundary of the anomaly detector. Experimental results, along with the theoretical analysis in Appendix A, support this claim.", "methods_and_evaluation_criteria": "Yes, the motivation and proposed solution are well-justified. The evaluation criteria are fair and aligned with established anomaly detection benchmarks.", "theoretical_claims": "Yes, the theoretical analysis in Appendix A demonstrates that the proposed solution outperforms reconstruction-based models.", "experimental_designs_or_analyses": "Yes, the experimental settings are fair, and the evaluation metrics align with existing graph-level anomaly detection literature. The study includes multiple perspectives, including both moderate-scale balanced and large-scale imbalanced experiments.", "relation_to_broader_scientific_literature": "AGDiff offers a novel approach to anomaly detection. It generates pseudo-anomalous data and trains a strong classifier to precisely define the decision boundary, tightly enclosing normal data. Additionally, it leverages a diffusion model with perturbation conditions to ensure pseudo-anomalies differ from normal data. This makes the method both innovative and effective.", "essential_references_not_discussed": "This paper presents a comprehensive discussion of both GLAD approaches and diffusion-based methods.", "other_strengths_and_weaknesses": "Strengths:\n1) The paper is well-written, and the idea is novel (refer to the comment in **\"Relation To Broader Scientific Literature\"**).\n2) Each module in the proposed method is well-designed with clear and justified motivation. The designed diffusion anomaly detection model is very different from the existing diffusion-based anomaly detection methods.\n3) Comprehensive experimental results demonstrate the method's effectiveness.\n4) Theoretical analysis is provided to support the claims.\n\nWeaknesses:\n1) How does the proposed method ensure a gap between real normal data and pseudo abnormal data? Are they definitively different? The authors should clarify this point.\n2) An analysis of the computational complexity is absent.\n3) In the theoretical analysis, why must A_2 perturb normal data before generating pseudo anomalous data? Why not directly use perturbed normal data to train the classifier? A more intuitive explanation, possibly with examples, would be helpful. \n4) The code used for the experiments is not provided.", "other_comments_or_suggestions": "There are some grammar and format errors, e.g., in line 142, \"Let … denotes\" should be \"Let … denote\". Authors should double-check the grammar carefully.", "questions_for_authors": "Please refer to Weaknesses.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "TO3SYS9gSg", "reviewer": "Reviewer_2Zh2", "summary": "In this paper, the authors proposed a novel GLAD method named AGDiff. AGDiff leverages diffusion models to generate pseudo-anomalous graphs, which addresses the challenge of anomaly scarcity in GLAD. Particularly, a latent diffusion process with perturbation conditions is proposed to generate diverse pseudo graph anomalies, and a joint training scheme is employed to integrate the training of pseudo anomaly generation and anomaly detection. Experiments on moderate-scale and large-scale imbalanced GLAD tasks demonstrated the effectiveness of AGDiff.", "questions": "", "limitations": "", "rating": 3, "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": "**We thank the reviewer for recognizing our work. Below are our responses to your concerns.**\n\n**To W1:** The condition vector $\\mathbf{c}$ is crucial for ensuring the generation quality of pseudo graph anomalies. By perturbing the initial latent embedding through a learnable perturbation transformation, $\\mathbf{c}$ injects additional variability into the latent diffusion process. This ensures that the denoising network is conditioned to deviate from purely \"normal\" reconstructions. We have evaluated the influence of $\\mathbf{c}$ via an Ablation Study (Table 3), where removing $\\mathbf{c}$ led to a substantial performance drop. In that case, the generated graphs may closely resemble normal graphs, making it more difficult for the anomaly detector to distinguish them and thus reducing its overall discriminative capability.\n\n**To W2:** AGDiff differs fundamentally from existing diffusion model-based methods [1,2,3]. Whereas existing approaches focus on modeling data normality, treating anomalies as outliers with significant reconstruction errors, AGDiff leverages the diffusion model to simulate subtle deviations from normal data and adaptively generate diverse pseudo-anomalous graphs that provide rich anomalous signals for refining the decision boundary learning. This proactive generation strategy facilitates the training of a powerful anomaly detector (as evidenced by the performance comparisons in Tables 1\\&2), enabling the model to better distinguish between normal and real anomalous graphs. We have included some discussions in Section 2.2, and we will elaborate further in the paper to emphasize our contributions.\n```\n[1] Wolleb, J., et al. Diffusion models for medical anomaly detection, MICCAI, 2022.\n[2] Tebbe, J., et al. Dynamic addition of noise in a diffusion model for anomaly detection, CVPR, 2024.\n[3] Li, J., et al. Diffgad: A diffusion-based unsupervised graph anomaly detector, ICLR 2025.\n```\n\n**To W3:** To clarify the effect of $T$ on the model's performance, we have conducted additional experiments by varying $T$ from 250 to 1500. The experimental results are as follows:\n\n$\\begin{matrix}\n\\\\hline\n\\text{Datasets}&\\text{Metrics}&T=250&T=500&T=750&T=1000&T=1250&T=1500\\\\\\\\\\hline\n\\text{MUTAG}&\\text{AUC}&91.52(7.84)&95.20(3.20)&\\bf95.84(3.84)& 95.83(2.15)&92.00(0.00)&92.00(0.00)\\\\\\\\\n&\\text{F1-Score}&88.00(4.00)&92.00(0.00)&\\bf94.00(2.00)& 89.45(1.37)&87.00(0.00)&87.00(0.00)\\\\\\\\\\hline\n\\text{ER\\\\_MD}&\\text{AUC}&86.61(4.38)&89.30(0.33)&84.48(2.17)&\\bf91.21 (1.84)&82.34(3.13)&82.18(0.91)\\\\\\\\\n&\\text{F1-Score}&78.30(6.60)&83.02(1.89)&79.25(5.66)&\\bf86.04 (2.26)&73.58(1.89)&73.58(1.89)\\\\\\\\\\hline\n\\end{matrix}$\n    \nAs seen above, the performance (e.g., on MUTAG) generally improves from $T=250$ (91.52\\% AUC) to $T=750$ (95.84\\% AUC) or $T=1000$ (95.83\\% AUC), with performance plateauing or declining when $T\\geq 1000$. A trend was similarly observed on ER_MD, which indicates that a low $T$ may be insufficient to generate high-quality pseudo graphs. Nevertheless, a high $T$ can also lead to over-diffusion, making the generated graphs excessively similar to normal graphs, which in turn diminishes the capability of the anomaly detector to differentiate them and increases computational cost as well. These findings highlight the importance of selecting appropriate $T$ to balance the generation quality and computational cost. We will add this experiment and relevant discussions to our paper.\n\n**To W4:** We have provided the implementation code of AGDiff at https://anonymous.4open.science/r/AGDiff-137F/. This link is fully anonymous, with some pre-trained models attached for reproducibility.\n\n**To Other Comments:** We will follow your suggestion to further discuss the limitations of our work in the conclusion, such as (1) Our method assumes a sufficiently representative distribution of normal graphs, which may not hold in shifting or highly heterogeneous environments. (2) While AGDiff can generate pseudo graph anomalies to enhance decision boundary training, it is currently limited to static graphs. Future work could explore solving challenging GLAD tasks in heterogeneous environments or dynamic graph settings.", "claims_and_evidence": "Yes. The key claims of this paper are well-supported by convincing evidence. For example, (1) Comparison results (Tables 1 and 2) demonstrate the consistent superiority of AGDiff over existing baselines across diverse datasets. (2) Scoring distribution analysis (Figure 2) shows overlap between normal and pseudo-anomalous graphs, with real anomalies distinctly separated, validating the claim that the generated pseudo-anomalous graphs resemble normal graphs with subtle deviations.", "methods_and_evaluation_criteria": "Yes. The proposed method is well-motivated, the latent diffusion process and joint training paradigm address the challenge of anomaly scarcity in GLAD problem. The evaluation criteria used in the experiment are suitable for GLAD.", "theoretical_claims": "Yes. The theoretical analysis in Appendix A intuitively demonstrated the superiority of the proposed method via the comparison between two algorithms (\\text{A}_{1} and \\text{A}_{2}).", "experimental_designs_or_analyses": "Yes. The experimental design is technically sound, with fair comparisons to graph kernels and GNN-based GLAD baselines. The authors conducted experiment on different GLAD scenarios and compared the proposed AGDiff with latest GLAD methods, which make the experimental results convincing.", "relation_to_broader_scientific_literature": "AGDiff bridges diffusion models and GLAD by leveraging a conditioned latent diffusion process to solve the anomaly scarcity problem in GLAD. It also contrasts with reconstruction-based GLAD methods, such as MUSE, by explicitly generating pseudo-anomalies.", "essential_references_not_discussed": "This paper has adequately discussed recent works in GLAD and diffusion models, and the authors also described the connection between the proposed method with other related works, which is sufficient to understand the key contribution of the paper.", "other_strengths_and_weaknesses": "*Pros:*\n- The paper is well-written, and the motivation is clearly illustrated. This work bridges a gap between diffusion modeling and graph-level anomaly detection, offering a novel perspective in the field.\n- The proposed perturbation conditioned latent diffusion process enables the model to eliminate reliance on labeled anomalies, making it more applicable to real-world domains.\n- Extensive experiments were conducted to demonstrate the effectiveness of the proposed method. Particularly, AGDiff exhibited superior performance in the large-scale imbalanced GLAD compared to the latest baselines.\n\n*Cons:*\n- In Eq. (10), the condition vector $\\textbf{c}$ is generated by perturbing the input. However, it is unclear what role $\\textbf{c}$ plays in the generation of the pseudo-anomalous graphs.\n- The difference between the proposed AGDiff and the diffusion-based anomaly detection approaches should be elaborated.\n- The experiment fixes the use of a diffusion process with $T=1,000$ steps, while the influence of varying $T$ on the anomaly detection performance is unclear.\n- The reproducibility of this work is relatively limited as the authors did not provide the implementation code for AGDiff.", "other_comments_or_suggestions": "The limitations of this work are not discussed in the conclusion. The authors are encouraged to provide additional discussion.", "questions_for_authors": "See Other Strengths And Weaknesses.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: The work introduces a novel method for Graph-Level Anomaly Detection. Strong empirical justification on the effectiveness of the method and its design is presented. 

The author did a great rebuttal that convinced two reviewers to increase their recommendation scores. After rebuttal, all four reviewers agree that the paper is above the acceptance bar of ICML.
Decision: Accept (spotlight poster)