Diffusion models represent a powerful class of generative models known for their solid theoretical foundations and remarkable performance across diverse tasks and domains. Existing node level diffusion methods synthesize nodes and edges within a graph, but are not designed to learn a robust generator from adversarially corrupted graphs. In this study, we introduce the Robust Graph Diffusion Model (RGDM), designed to generate labeled synthetic graph structures consisting of nodes and edges that integrate seamlessly into a given graph. The RGDM consists of a Robust Graph Autoencoder (RGAE) and a Latent Diffusion Model (LDM). Leveraging an edge selection mechanism and an innovative low-rank regularization on the latent feature, the RGDM produces clean and high-quality synthetic graph structures, even when trained on graphs subject to adversarial attacks. Comprehensive experimental evaluations reveal that Graph Neural Networks (GNNs) trained on the augmented graph, which is formed by merging the original attacked graph with the synthetic graph structures, exhibit significantly improved robustness against various graph adversarial attacks in the context of semi-supervised node classification. The code of the RGDM is available at https://github.com/Statistical-Deep-Learning/RGDM.
Figures & tables
Figure 1: Illustration of the 2-hop neighborhood of a real node and a synthetic node in the augmented graph. Figure 5 in Section F.10 illustrates the t-SNE visualization of the augmented graph.
Figure 2: Figure (a) illustrates the synthetic node generation process in Robust Graph Diffusion Model. Figure (b) illustrates the structure of the Sparse Hierarchical Edge Decoder (SHED).
Dataset
Ptb Rate (%)
GCN
GCORNs
HANG
STABLE
Pro-GNN
SG-GSR
Cora
0 (clean)
83.5 ± 0.4
82.6 ± 0.5
80.1 ± 0.3
84.7 ± 0.5
83.0 ± 0.2
85.5 ± 1.3
15
65.1 ± 0.7
72.6 ± 1.2
72.9 ± 1.0
74.4 ± 0.9
76.4 ± 1.3
78.5 ± 1.6
25
47.5 ± 1.9
69.5 ± 1.9
68.7 ± 1.9
69.6 ± 0.6
69.7 ± 1.7
77.8 ± 1.3
Citeseer
0 (clean)
72.0 ± 0.6
72.6 ± 0.4
73.3 ± 0.4
74.8 ± 0.5
73.3 ± 0.7
75.8 ± 1.4
15
64.5 ± 1.1
65.5 ± 1.0
70.8 ± 0.9
67.5 ± 0.4
72.0 ± 1.1
73.1 ± 1.4
25
56.9 ± 1.1
65.2 ± 1.3
66.4 ± 1.6
65.6 ± 1.9
69.0 ± 1.8
72.7 ± 1.4
Table 1: Metattack accuracy ± marginal SD (%). Parentheses give the augmentation gain. A further ± is its SD from the separate paired evaluation (Table 26 ). A 0% rate is a clean graph. Bold and underline mark the best and second best results across both panels for each setting. Complete results appear in Table 10 .
Dataset
Budget
GCN
GCORNs
HANG
STABLE
Pro-GNN
SG-GSR
Cora
0 (clean)
81.4 ± 1.0
82.6 ± 0.4
80.8 ± 1.3
85.3 ± 1.8
84.8 ± 0.6
85.5 ± 1.7
3
68.0 ± 1.7
73.2 ± 0.7
73.1 ± 1.9
73.8 ± 1.8
72.4 ± 0.5
74.9 ± 1.2
5
55.5 ± 1.7
66.9 ± 1.1
68.8 ± 1.6
68.4 ± 1.6
66.9 ± 0.7
68.0 ± 1.5
Citeseer
0 (clean)
81.0 ± 1.4
81.9 ± 1.2
81.1 ± 1.1
82.4 ± 1.8
82.1 ± 0.8
82.8 ± 1.2
3
64.0 ± 1.7
78.1 ± 1.1
77.1 ± 1.5
80.9 ± 1.5
79.7 ± 2.0
81.7 ± 1.2
5
47.6 ± 1.2
71.7 ± 1.8
73.5 ± 1.5
72.5 ± 1.5
71.3 ± 2.0
73.8 ± 1.0
Table 2: Nettack accuracy ± marginal SD (%), with augmentation gains in parentheses. Budget 0 is a clean graph. The highlighting convention is that of Table 1 . Complete results appear in Table 11 .
Table 3: Ablation study on the sparsification loss and the low-rank regularization term.
Method
Cora
Citeseer
Polblogs
Pubmed
GCN
47.53
56.94
49.23
75.50
iGraphMix (GCN) ( Jeong et al., 2024 )
53.25
57.11
51.65
76.10
ImGAGN (GCN) ( Qu et al., 2021 )
53.58
56.89
50.95
75.32
Graphsmote (GCN) ( Zhao et al., 2021a )
55.10
58.06
52.44
76.25
SNS (GCN) ( Gao et al., 2023 )
58.35
59.17
54.03
78.28
DoG (GCN) ( Wang et al., 2025 )
59.40
60.10
54.70
79.20
Table 4: Comparisons between RGDM and existing node-level graph augmentation methods. The study is performed for Metattack with a perturbation rate of 25% .
Configuration
Cora
Citeseer
Polblogs
Pubmed
SG-GSR (no augmentation)
77.8
72.7
87.8
87.2
DoG augmentation (BLND)
75.6
71.0
85.3
85.1
+ Edge selection
76.6
72.1
86.3
85.9
+ Latent TNN (RGDM with BLND)
77.4
73.1
87.2
86.6
+ SHED (full RGDM)
79.1
75.3
88.8
88.6
Table 5: Successive generator components. SG-GSR and 25% Metattack are fixed. Accuracy in percent.
Dataset
0% (clean)
15%
25%
Chameleon
72.31 / 74.02
71.87 / 72.98
70.03 / 72.41
Actor
38.87 / 41.80
36.79 / 39.01
35.37 / 37.90
Table 6: Heterophilic graphs under Metattack. Each entry is LHS / RGDM(LHS) accuracy (%).
Dataset
Final graph attack
Through edge selection
Cora
74.8 / 77.8
74.5 / 76.9
Citeseer
69.5 / 73.4
69.2 / 72.4
Polblogs
84.7 / 87.6
84.4 / 86.6
Pubmed
84.9 / 87.2
84.6 / 86.3
Table 7: Adaptive Metattack: baseline SG-GSR / RGDM(SG-GSR) accuracy (%). The budget is fixed in absolute edge flips.
Dataset
Training (min)
Generation (s/node)
Pubmed
153 / 480
0.073 / 0.080
ogbn-arxiv
452 / 2511
0.15 / 0.49
Table 8: SHED / global decoder timings: RGAE training and complete synthetic node generation.
Appendix figures & tables32 assets
Supplementary material from the paper’s appendix.
Appendix
Datasets
# Node
# Edge
Classes
Features
Cora
2,485
5,069
7
1,433
Citeseer
2,110
3,668
6
3,703
Polblogs
1,222
16,714
2
1,222
Pubmed
19,717
44,338
3
500
ogbn-arxiv
169,343
1,166,243
40
128
Reddit
232,965
11,606,919
41
602
Appendix
Table 9: Statistics of the datasets.
Figure 3: Eigen-projection (left) and concentration ratio (right) of the ground truth label and the adversarial noise on Pubmed. The study is performed for Metattack with a perturbation ratio of 25% . By the rank r=r0=0.2min{N,D′} , the signal concentration ratio of the ground truth label is 0.784 . Results on Cora and Citeseer are illustrated in Figure 4 in Section F.1 .
Figure 4: Eigen-projection (first row) and concentration ratio (second row) of the ground truth label and the adversarial noise on Cora, Citeseer, and Pubmed. The study in this figure is performed for Metattack with a perturbation ratio of 25% . By the rank r=r0=0.2min{N,D′} , the signal concentration ratios of the ground truth label for Cora, Citeseer, and Pubmed are 0.844 , 0.809 , and 0.784 respectively.
Dataset
Ptb Rate (%)
GCN
GAT
RGCN
GCN-SVD
GraphBel
UAG
GCORNs
GADC
HANG
Pro-GNN
RGDM (GCN)
RGDM (HANG)
RGDM (Pro-GNN)
Cora
0
83.50 ± 0.44
83.97 ± 0.65
83.09 ± 0.44
80.63 ± 0.45
83.42 ± 0.52
82.05 ± 0.51
82.56 ± 0.48
83.22 ± 0.61
80.07 ± 0.32
82.98 ± 0.23
85.23 ± 0.44 ( ↑1.73 )
82.31 ± 0.51 ( ↑2.24 )
84.29 ± 0.52 ( ↑1.31 )
5
76.55 ± 0.79
80.44 ± 0.74
77.42 ± 0.39
78.39 ± 0.54
82.78 ± 0.39
79.13 ± 0.59
75.91 ± 1.88
75.68 ± 1.10
78.12 ± 0.72
82.27 ± 0.45
80.19 ± 0.39 ( ↑3.64 )
81.04 ± 0.59 ( ↑2.92 )
83.19 ± 0.39 ( ↑0.92 )
10
70.39 ± 1.28
75.61 ± 0.59
72.22 ± 0.38
71.47 ± 0.83
77.91 ± 0.86
75.16 ± 0.76
74.63 ± 1.02
73.70 ± 1.17
75.96 ± 0.62
79.03 ± 0.59
76.73 ± 0.38 ( ↑6.34 )
78.03 ± 0.76 ( ↑2.07 )
81.16 ± 0.86 ( ↑2.13 )
15
65.10 ± 0.71
69.78 ± 1.28
66.82 ± 0.39
66.69 ± 1.18
76.01 ± 1.12
71.03 ± 0.64
72.57 ± 1.24
71.39 ± 1.22
72.89 ± 0.96
76.40 ± 1.27
69.37 ± 0.39 ( ↑4.27 )
76.39 ± 0.64 ( ↑3.50 )
78.29 ± 1.12 ( ↑1.89 )
20
59.56 ± 1.72
59.94 ± 0.92
59.27 ± 0.37
58.94 ± 1.13
68.78 ± 1.84
65.71 ± 0.89
71.94 ± 1.51
71.20 ± 1.49
70.36 ± 1.09
73.32 ± 1.56
65.97 ± 0.37 ( ↑6.41 )
73.25 ± 0.89 ( ↑2.89 )
74.85 ± 1.84 ( ↑1.53 )
25
47.53 ± 1.91
54.78 ± 0.74
50.51 ± 0.78
52.06 ± 1.19
56.54 ± 1.58
60.82 ± 1.08
69.48 ± 1.94
68.29 ± 1.36
68.72 ± 1.87
69.72 ± 1.69
61.42 ± 0.78 ( ↑13.89 )
70.44 ± 1.08 ( ↑1.72 )
72.31 ± 1.58 ( ↑2.59 )
Appendix
Table 10: Node classification performance (Accuracy ± Std) under the non-targeted poisoning attack (Metattack) [ 101 ] . The improvements of the RGDM over the corresponding baselines are attached in parentheses after the results of the RGDM.
Dataset
Attack Budget
GCN
GAT
RGCN
GCN-SVD
GraphBel
UAG
GCORNs
GADC
HANG
Pro-GNN
RGDM (GCN)
RGDM (HANG)
RGDM (Pro-GNN)
Cora
0
81.43 ± 1.04
82.14 ± 1.13
81.34 ± 1.55
81.10 ± 1.34
71.55 ± 1.01
82.34 ± 1.08
82.61 ± 0.41
81.36 ± 1.83
80.75 ± 1.27
84.78 ± 0.59
83.43 ± 1.08 ( ↑2.00 )
82.10 ± 1.34 ( ↑1.35 )
86.00 ± 1.13 ( ↑1.22 )
1
75.06 ± 1.02
76.04 ± 1.08
76.75 ± 1.71
77.23 ± 1.82
63.73 ± 1.25
81.75 ± 1.16
81.05 ± 1.14
80.05 ± 1.53
76.99 ± 1.16
83.85 ± 0.51
78.41 ± 1.16 ( ↑3.35 )
80.39 ± 1.82 ( ↑3.40 )
84.79 ± 1.08 ( ↑0.94 )
2
70.60 ± 1.10
70.24 ± 1.43
70.96 ± 1.14
72.53 ± 1.60
62.41 ± 1.94
77.96 ± 1.84
78.47 ± 1.32
75.90 ± 1.29
76.51 ± 1.60
78.65 ± 0.66
73.79 ± 1.84 ( ↑3.19 )
79.14 ± 1.60 ( ↑2.63 )
80.02 ± 1.43 ( ↑1.37 )
3
67.95 ± 1.72
65.54 ± 1.34
66.51 ± 1.60
66.75 ± 1.54
61.20 ± 1.08
72.51 ± 1.14
73.17 ± 0.74
71.94 ± 1.45
73.13 ± 1.85
72.40 ± 0.53
70.46 ± 1.14 ( ↑2.51 )
76.31 ± 1.54 ( ↑3.18 )
74.31 ± 1.34 ( ↑1.91 )
4
61.57 ± 1.47
61.69 ± 0.90
59.28 ± 1.68
60.72 ± 1.63
56.51 ± 1.72
70.28 ± 1.52
71.26 ± 0.62
70.93 ± 1.19
72.53 ± 1.14
70.12 ± 0.66
64.37 ± 1.52 ( ↑2.80 )
75.12 ± 1.63 ( ↑2.59 )
72.79 ± 0.90 ( ↑2.67 )
5
55.54 ± 1.66
58.31 ± 1.03
55.30 ± 1.66
57.71 ± 1.82
51.93 ± 1.77
66.30 ± 1.21
66.89 ± 1.08
64.49 ± 1.42
68.80 ± 1.55
66.89 ± 0.73
59.44 ± 1.21 ( ↑3.90 )
69.81 ± 1.82 ( ↑1.01 )
69.81 ± 1.03 ( ↑2.92 )
Appendix
Table 11: Node classification performance (Accuracy ± Std) under targeted attack (Nettack) [ 100 ] . The improvements of RGDM over the corresponding baselines are attached in parentheses after the results of the RGDM.
Dataset
Ptb Rate (%)
GCN
GAT
RGCN
GCN-SVD
GraphBel
UAG
GCORNs
GADC
HANG
Pro-GNN
RGDM(GCN)
RGDM(HANG)
RGDM(Pro-GNN)
Cora
0
83.50 ± 0.44
83.97 ± 0.65
83.09 ± 0.44
80.63 ± 0.45
83.42 ± 0.52
82.05 ± 0.51
82.63 ± 0.47
83.21 ± 0.72
80.07 ± 0.32
82.98 ± 0.23
85.23 ± 0.44 ( ↑1.73 )
82.31 ± 0.51 ( ↑2.24 )
84.29 ± 0.52 ( ↑1.31 )
5
75.50 ± 0.44
76.97 ± 0.65
75.04 ± 1.32
75.82 ± 1.24
77.01 ± 1.33
76.22 ± 1.24
75.96 ± 1.81
76.83 ± 1.25
76.99 ± 1.52
77.63 ± 1.85
77.92 ± 1.08 ( ↑2.42 )
79.39 ± 1.33 ( ↑2.40 )
81.10 ± 1.16 ( ↑3.47 )
10
72.02 ± 1.32
74.10 ± 1.84
73.05 ± 1.25
74.00 ± 1.76
74.00 ± 1.57
76.00 ± 1.76
74.67 ± 1.03
75.90 ± 1.84
76.99 ± 1.52
77.63 ± 1.85
74.22 ± 1.43 ( ↑2.20 )
79.44 ± 1.57 ( ↑2.45 )
80.36 ± 1.84 ( ↑2.73 )
15
69.42 ± 1.71
70.55 ± 1.69
71.61 ± 1.34
72.90 ± 1.46
72.79 ± 1.26
74.90 ± 1.33
72.58 ± 1.27
74.34 ± 1.52
75.63 ± 1.59
75.40 ± 1.32
72.42 ± 1.34 ( ↑3.00 )
76.92 ± 1.26 ( ↑1.29 )
76.57 ± 1.14 ( ↑1.17 )
20
67.61 ± 1.02
68.84 ± 1.33
67.87 ± 1.22
70.00 ± 1.83
70.55 ± 1.17
71.85 ± 1.22
71.99 ± 1.54
72.06 ± 1.80
72.15 ± 1.27
71.32 ± 1.79
71.61 ± 0.90 ( ↑4.00 )
74.35 ± 1.17 ( ↑2.20 )
74.44 ± 1.52 ( ↑3.12 )
25
64.81 ± 1.14
65.51 ± 1.45
66.02 ± 1.39
67.89 ± 1.21
66.32 ± 1.07
68.03 ± 1.39
69.47 ± 1.98
68.92 ± 1.27
69.10 ± 1.33
68.72 ± 1.50
69.53 ± 1.03 ( ↑4.72 )
71.67 ± 1.07 ( ↑2.57 )
72.07 ± 1.21 ( ↑3.35 )
Appendix
Table 12: Node classification performance (Accuracy ± Std) under Topology Attack [ 82 ] . The improvements of the RGDM over the corresponding baselines are attached in parentheses after the results of the RGDM.
Data
Cora
Citeseer
Polblogs
Pubmed
Original Attacked Graph
12.10 ± 0.45
7.53 ± 0.22
8.26 ± 0.37
6.11 ± 0.38
iGraphMix [ 34 ]
13.44 ± 0.33
9.02 ± 0.42
10.75 ± 0.44
7.65 ± 0.38
ImGAGN [ 55 ]
13.10 ± 0.38
7.96 ± 0.42
9.86 ± 0.43
6.95 ± 0.27
Graphsmote [ 93 ]
13.52 ± 0.42
8.95 ± 0.22
10.60 ± 0.27
7.45 ± 0.51
SNS [ 22 ]
13.35 ± 0.42
7.88 ± 0.27
9.30 ± 0.85
6.74 ± 0.41
Baseline DDPM
13.28 ± 0.40
8.82 ± 0.26
10.25 ± 0.39
7.25 ± 0.41
Appendix
Table 13: Frechet Node Distance (FND) to the nodes in the base partition of the original clean graph. The mean and standard deviation of the FND scores computed with 10 different random splits of the base partition and the test partition in the original clean graph are reported. The evaluation is performed for Metattack with a perturbation rate of 25% . The FND score for the original clean graph is computed between the nodes in the test partition and the nodes in the base partition of the original clean graph.
Data
Cora
Citeseer
Polblogs
Pubmed
Original Attacked Graph
10.32 ± 0.42
7.83 ± 0.28
8.92 ± 0.39
6.53 ± 0.37
iGraphMix [ 34 ]
11.25 ± 0.28
8.42 ± 0.43
9.63 ± 0.44
7.11 ± 0.27
ImGAGN [ 55 ]
11.05 ± 0.38
8.04 ± 0.26
8.21 ± 0.51
7.16 ± 0.79
Graphsmote [ 93 ]
11.13 ± 0.29
8.16 ± 0.51
9.32 ± 0.41
7.18 ± 0.44
SNS [ 22 ]
11.05 ± 0.38
8.04 ± 0.26
8.21 ± 0.51
7.16 ± 0.79
Baseline DDPM ( K=⌈dave/4⌉ )
12.03 ± 0.45
8.72 ± 0.31
10.77 ± 0.40
7.93 ± 0.42
Appendix
Table 14: Frechet Edge Distance (FED) to the edges in the base partition of the original clean graph. The mean and standard deviation of the FED scores computed with 10 different random splits of the base partition and the test partition in the original clean graph are reported. The evaluation is performed for Metattack with a perturbation rate of 25% . The FED score for the original clean graph is computed between the edges in the test partition and the edges in the base partition of the original clean graph.
RGAE training (min)
Generation (s/node)
Dataset
SHED
Global
SHED
Global
Cora
20
29
0.066
0.089
Citeseer
23
30
0.067
0.086
Polblogs
65
88
0.069
0.090
Pubmed
153
480
0.073
0.080
ogbn-arxiv
452
2511
0.15
0.49
Appendix
Table 15: SHED versus a global decoder on one NVIDIA A100. The generation measurement includes LDM sampling and decoding.
Datasets
RGDM Training Time (minutes)
Generation Time (s/sample)
RGAE
LDM
Cora
20
39
0.066
Citeseer
23
41
0.067
Polblogs
65
31
0.069
Pubmed
153
154
0.073
Appendix
Table 16: Time for the training of the RGDM and data generation with the RGDM on different datasets.
Datasets
Cross-validation Time (minutes)
RGDM (GCN)
RGDM (SG-GSR)
RGDM (Pro-GNN)
Cora
1.1
3.5
43.3
Citeseer
1.0
3.4
38.5
Polblogs
1.6
3.9
26.9
Pubmed
9.4
20.5
176.5
Appendix
Table 17: Time for selecting the optimal number of synthetic nodes N′ with cross-validation.
Dataset
Ptb Rate (%)
RGDM (GCN)
RGDM (SG-GSR)
RGDM (Pro-GNN)
Cora
0
2×∣VL∣
1×∣VL∣
2×∣VL∣
5
2×∣VL∣
1×∣VL∣
2×∣VL∣
10
2×∣VL∣
1×∣VL∣
2×∣VL∣
15
3×∣VL∣
1×∣VL∣
3×∣VL∣
20
3×∣VL∣
2×∣VL∣
3×∣VL∣
25
5×∣VL∣
5×∣VL∣
5×∣VL∣
Appendix
Table 18: The number of synthetic nodes N′ ( ×∣VL∣ ) selected for Metattack, where VL is the labeled nodes of the original graph.
Dataset
Attack Budget
RGDM (GCN)
RGDM (SG-GSR)
RGDM (Pro-GNN)
Cora
0
2×∣VL∣
1×∣VL∣
2×∣VL∣
1
3×∣VL∣
2×∣VL∣
2×∣VL∣
2
3×∣VL∣
2×∣VL∣
2×∣VL∣
3
3×∣VL∣
2×∣VL∣
3×∣VL∣
4
3×∣VL∣
3×∣VL∣
3×∣VL∣
5
4×∣VL∣
3×∣VL∣
3×∣VL∣
Appendix
Table 19: The number of synthetic nodes N′ ( ×∣VL∣ ) for Nettack, where VL is the labeled nodes of the original graph.
Dataset
Ptb Rate (%)
RGDM (GCN)
RGDM (SG-GSR)
RGDM (Pro-GNN)
Cora
0
1×∣VL∣
1×∣VL∣
1×∣VL∣
5
1×∣VL∣
1×∣VL∣
1×∣VL∣
10
2×∣VL∣
2×∣VL∣
2×∣VL∣
15
2×∣VL∣
1×∣VL∣
2×∣VL∣
20
2×∣VL∣
2×∣VL∣
3×∣VL∣
25
2×∣VL∣
2×∣VL∣
2×∣VL∣
Appendix
Table 20: The number of synthetic nodes N′ ( ×∣VL∣ ) for Topology Attack, where VL is the labeled nodes of the original graph.
Dataset
Ptb Rate (%)
GCN
RGDM (GCN)
ogbn-arxiv
0
72.82 ± 1.32
74.48 ± 1.15 ( ↑1.66 )
10
62.25 ± 1.23
64.50 ± 1.35 ( ↑2.25 )
20
54.95 ± 1.44
56.17 ± 1.66 ( ↑1.22 )
Reddit
0
93.52 ± 1.17
95.44 ± 1.42 ( ↑1.92 )
10
82.62 ± 1.32
84.73 ± 1.12 ( ↑2.11 )
20
74.53 ± 1.57
75.99 ± 1.22 ( ↑1.46 )
Appendix
Table 21: Node classification performance (Accuracy ± Std) under the adversarial attack by the improved DICE [ 44 ] . The improvements of the RGDM over the baseline are attached in parentheses.
Method
ogbn-arxiv
Reddit
GCN
54.95
74.53
RGDM without edge selection
55.30
75.00
RGDM (full)
56.17
75.99
Appendix
Table 22: Edge selection ablation on large graphs under 20% improved DICE, with GCN fixed. Accuracy (%).
τ
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Accuracy
72.12
72.16
72.30
72.29
72.31
72.28
72.24
72.22
72.25
Appendix
Table 23: Sensitivity analysis on the temperature for edge selection τ . The study is performed by using RGDM (Pro-GNN) on Cora with 25% of Metattack.
K
20
40
60
80
100
120
150
200
M=⌈N/K⌉
125
63
42
32
25
21
17
13
Generation Time (s/sample)
0.075
0.070
0.068
0.067
0.066
0.067
0.068
0.071
Accuracy
72.12
72.20
72.26
72.29
72.31
72.28
72.24
72.20
Appendix
Table 24: Sensitivity analysis on the number of clusters K in SHED. The study is performed by using RGDM (Pro-GNN) on Cora with 25% of Metattack.
Dataset
Ptb Rate (%)
LHS
RGDM (LHS)
Chameleon
0
72.31 ± 1.32
74.02 ± 1.13 ( ↑1.71 )
15
71.87 ± 1.61
72.98 ± 1.11 ( ↑1.11 )
25
70.03 ± 1.85
72.41 ± 1.66 ( ↑2.38 )
Actor
0
38.87 ± 1.43
41.80 ± 1.42 ( ↑2.93 )
15
36.79 ± 1.11
39.01 ± 1.12 ( ↑2.22 )
25
35.37 ± 1.12
37.90 ± 1.01 ( ↑2.53 )
Appendix
Table 25: Node classification performance (Accuracy ± Std) under the non-targeted poisoning attack (Metattack) [ 101 ] . The improvements of the RGDM over the baseline are attached in parentheses.
Figure 5: Illustration of the augmented graph after adding the synthetic graph structures into the original graph on Cora. The RGDM is trained on Cora under Metattack with a perturbation rate of 25% . The figure on the right illustrates the t-SNE visualization of the node features for both the real nodes in the original clean graph and the synthetic nodes. The figure on the left illustrates the 2-hop neighborhood of a real node and a synthetic node that have similar node features, evidenced by the t-SNE visualization in the augmented graph. It is observed that the synthetic node shares the same neighbors as the real node.
Dataset
Ptb (%)
GCN
Pro-GNN
SG-GSR
Cora
0
1.7±0.3
1.3±0.3
0.4±0.1
Cora
15
4.3±0.5
1.9±0.4
1.5±0.3
Cora
25
13.9±0.7
2.6±0.4
1.3±0.3
Citeseer
15
4.2±0.5
1.7±0.4
2.9±0.4
Citeseer
25
5.9±0.5
1.2±0.3
2.6±0.4
Polblogs
15
4.9±0.5
2.0±0.4
1.1±0.3
Appendix
Table 26: Reported Metattack mean gain ± paired SD over 10 shared attack seeds (percentage points). Only rows with reported paired SD are included.
Dataset
Ptb (%)
RGDM (GCN)
RGDM (Pro-GNN)
RGDM (SG-GSR)
Cora
0
≤0.042
≤0.027
≤0.016
5
0.038
0.024
0.013
10
0.033
0.021
0.012
15
≤0.029
≤0.017
≤0.010
20
0.025
0.015
0.009
25
≤0.021
≤0.012
≤0.008
Appendix
Table 27: Reported significance levels with each backbone fixed: Metattack. For rows with paired summaries in Table 26 , ≤ denotes a conservative upper threshold, not an exact p value reconstructed from rounded moments. Remaining entries are reported p values.
Dataset
Budget
RGDM (GCN)
RGDM (Pro-GNN)
RGDM (SG-GSR)
Cora
0
0.041
0.025
0.015
1
0.036
0.023
0.011
2
0.032
0.019
0.010
3
0.027
0.016
0.008
4
0.022
0.013
0.007
5
0.019
0.011
0.006
Appendix
Table 28: Reported significance levels with each backbone fixed: Nettack. Continued from the preceding panel. Entries are the reported p values.
Dataset
Ptb (%)
RGDM (GCN)
RGDM (Pro-GNN)
RGDM (SG-GSR)
Cora
0
0.043
0.029
0.017
5
0.039
0.025
0.012
10
0.035
0.020
0.011
15
0.030
0.018
0.009
20
0.026
0.014
0.008
25
0.022
0.012
0.007
Appendix
Table 29: Reported significance levels with each backbone fixed: Topology Attack. Continued from the preceding panel. Entries are the reported p values.
Method
Accuracy ( % )
Pro-GNN
69.7
RGDM (Purification)
71.0
RGDM (GDA)
72.3
RGDM (GDA + Purification)
72.9
Appendix
Table 30: Study on the effectiveness of graph purification and GDA by RGDM. The evaluation is conducted on Cora under Metattack with 25% perturbation rate.
Datasets
GDDM [ 27 ]
DiffSP [ 49 ]
RGDM (SG-GSR)
p-value
Cora
77.2±0.3
76.8±0.5
79.1±1.6
0.0022
Citeseer
71.6±0.5
71.8±0.2
75.3±1.0
0.0012
Polblogs
84.8±0.8
85.6±0.5
88.8±1.8
0.0004
Pubmed
85.9±0.6
86.8±0.4
88.6±1.3
0.0017
Appendix
Table 31: Comparison of classification accuracy ( ± Std) and p-values across different datasets between RGDM and diffusion-based graph purification methods.
# Synthetic Nodes ( ×∣VL∣ )
1
2
3
4
5
6
7
8
9
10
Accuracy (%)
70.5
71.0
71.9
72.2
72.3
72.1
72.0
71.7
71.4
71.2
Appendix
Table 32: Performance of RGDM (Pro-GNN) under Metattack with varying numbers of synthetic nodes. The perturbation rate is 25% .
Method
Accuracy ( % )
Pro-GNN
69.7
DDPM (Pro-GNN)
68.2
RGDM (Pro-GNN)
72.3
Appendix
Table 33: Performance comparison of Pro-GNN on augmented graph with synthetic graph structures generated by DDPM and RGDM. The study is performed on Cora under Metattack with a perturbation rate of 25% .
Label Ratio
2.5%
5%
7.5%
10%
20%
40%
60%
Pro-GNN
62.5
65.6
67.5
69.7
73.8
75.2
76.6
RGDM (Pro-GNN)
64.8
68.0
69.3
72.3
75.9
77.6
78.4
Appendix
Table 34: Performance comparison of Pro-GNN and RGDM (Pro-GNN) under different label ratios on Cora under 25% Metattack.
Dataset
Cora
Citeseer
Polblogs
Pubmed
RGDM (HGAE from LR-FGDM)
76.8
72.5
86.7
86.0
RGDM (BLND)
77.4
73.1
87.2
86.6
RGDM
79.1
75.3
88.8
88.6
Appendix
Table 35: Hierarchical reconstruction comparison: SHED, BLND from DoG [ 74 ] , and the HGAE variant from LR-FGDM [ 75 ] . SG-GSR is used as the base GNN under Metattack with 25% perturbation.
Dataset
SG-GSR
RGDM (SG-GSR)
p -value
Cora
74.8±2.4
77.8±1.8
0.006
Citeseer
69.5±2.6
73.4±2.1
0.003
Polblogs
84.7±2.5
87.6±2.2
0.008
Pubmed
84.9±2.7
87.2±2.4
0.012
Appendix
Table 36: Adaptive attack evaluation under Metattack [ 101 ] with 25% perturbation rate. The adaptive attacker is aware of the defense and attacks the final augmented graph used for training SG-GSR. The p -values are computed between SG-GSR and RGDM (SG-GSR).
Dataset
SG-GSR
RGDM (SG-GSR)
Gain (points)
Cora
74.5
76.9
2.4
Citeseer
69.2
72.4
3.2
Polblogs
84.4
86.6
2.2
Pubmed
84.6
86.3
1.7
Appendix
Table 37: Adaptive Metattack differentiating through the relaxed edge selection mask with the same absolute edge flip budget and τ=0.5 . Mean accuracy (%).
Graph Neural Networks (GNNs) are effective for modeling relational data but are vulnerable to label poisoning, where a small number of corrupted training labels can propagate errors across the graph via message passing. Despite this risk, defenses against label poisoning remain underexplored: existing methods are primarily designed for label noise and often rely on robust losses or heuristic data cleaning that fail to distinguish adversarial poisoning from naturally hard examples. In this paper, we propose CoLAT (Contrastive Label-flipping for Adversarial Training), a novel contrastive adversarial training framework tailored for robust node classification on graphs. The core of our approach is a structure-aware detection model that uses contrastive learning to identify label-structure inconsistencies. Unlike prior contrastive methods that focus on representation learning, CoLAT leverages contrastive embeddings to select high-risk nodes that guide adversarial label-flipping during training. This alternating optimization not only performs structure-aware adversarial training but also implicitly sanitizes some corrupted labels, improving robustness against diverse attacks from the literature. Extensive experiments on multiple benchmarks show that CoLAT consistently outperforms existing defenses under various poisoning intensities while scaling efficiently to large graphs.
Manshika Charvi Bissessur, Melis Ilayda Bal, Michael Muehlebach
University of Oxford · Max Planck Institute for Intelligent Systems, Tübingen, Germany · LIONS – École Polytechnique Fédérale de Lausanne +1
Defending Graph Neural Networks (GNNs) against adversarial attacks requires balancing accuracy and robustness, a trade-off often mishandled by traditional methods like adversarial training that intertwine these conflicting objectives within a single classifier. To overcome this limitation, we propose a self-supervised adversarial purification framework. We separate robustness from the classifier by introducing a dedicated purifier, which cleanses the input data before classification. In contrast to prior adversarial purification methods, we propose GPR-GAE, a novel graph auto-encoder (GAE), as a specialized purifier trained with a self-supervised strategy, adapting to diverse graph structures in a data-driven manner. Utilizing multiple Generalized PageRank (GPR) filters, GPR-GAE captures diverse structural representations for robust and effective purification. Our multi-step purification process further facilitates GPR-GAE to achieve precise graph recovery and robust defense against structural perturbations. Experiments across diverse datasets and attack scenarios demonstrate the state-of-the-art robustness of GPR-GAE, showcasing it as an independent plug-and-play purifier for GNN classifiers.
Woohyun Lee, Hogun Park
Department of Computer Science and Engineering, Sungkyunkwan University, Suwon, South Korea.
Graph neural networks frequently encounter significant performance degradation when confronted with structural noise or non-homophilous topologies. To address these systemic vulnerabilities, we present AdvSynGNN, a comprehensive architecture designed for resilient node-level representation learning. The proposed framework orchestrates multi-resolution structural synthesis alongside contrastive objectives to establish geometry-sensitive initializations. We develop a transformer backbone that adaptively accommodates heterophily by modulating attention mechanisms through learned topological signals. Central to our contribution is an integrated adversarial propagation engine, where a generative component identifies potential connectivity alterations while a discriminator enforces global coherence. Furthermore, label refinement is achieved through a residual correction scheme guided by per-node confidence metrics, which facilitates precise control over iterative stability. Empirical evaluations demonstrate that this synergistic approach effectively optimizes predictive accuracy across diverse graph distributions while maintaining computational efficiency. The study concludes with practical implementation protocols to ensure the robust deployment of the AdvSynGNN system in large-scale environments.