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arxiv: 2501.11568 · v2 · submitted 2025-01-20 · 💻 cs.LG

Graph Defense Diffusion Model

Xin He , Wenqi Fan , Yili Wang , Chengyi Liu , Rui Miao , Xin Juan , Xin Wang This is my paper

Pith reviewed 2026-05-23 04:48 UTC · model grok-4.3

classification 💻 cs.LG
keywords graph neural networksadversarial defensediffusion modelsgraph purificationadversarial attacksgraph structure
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The pith

A diffusion model defends graph neural networks by iteratively adding and removing edge noise to restore original structures after attacks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents GDDM as a purification approach for graphs under adversarial attack. Existing methods filter graphs using heuristics but cannot flexibly handle both targeted and non-targeted attacks at once. GDDM applies the forward and reverse processes of diffusion models to add and remove noise in steps that mirror how attacks are built. Two added components keep the generated graph close to the original scope and strip out leftover impurities. Tests on three real-world datasets show better defense performance than prior purification techniques.

Core claim

GDDM is a flexible purification method that leverages the denoising and modeling capabilities of diffusion models. The iterative nature of diffusion models aligns well with the stepwise process of adversarial attacks, making them particularly suitable for defense. By iteratively adding and removing noises (edges), GDDM effectively purifies attacked graphs, restoring their original structures and features. The model includes a Graph Structure-Driven Refiner and a Node Feature-Constrained Regularizer, uses tailored denoising strategies for different attacks, and transfers across similar datasets without retraining.

What carries the argument

Graph Defense Diffusion Model (GDDM) with Graph Structure-Driven Refiner that preserves basic graph fidelity during denoising and Node Feature-Constrained Regularizer that removes residual impurities.

If this is right

  • GDDM can defend against both targeted and non-targeted attacks simultaneously by using tailored denoising strategies.
  • The model scales to similar datasets without retraining by leveraging its structural properties.
  • Purification quality improves through the combination of structure preservation and feature constraint during denoising.
  • Overall defense robustness increases compared with heuristic purification methods on the evaluated datasets.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same iterative noise mechanism might apply to defending other structured data such as molecular graphs or knowledge graphs.
  • Transfer without retraining could enable rapid deployment when new but related graphs appear in production systems.
  • Combining the refiner and regularizer with existing attack-detection modules might create layered defenses.

Load-bearing premise

The iterative denoising process of diffusion models aligns with the stepwise nature of adversarial attacks and can restore original graph structures without introducing new distortions.

What would settle it

An experiment in which GDDM applied to an attacked graph produces lower downstream task accuracy than the attacked graph itself or fails to match clean-graph performance on a dataset outside the three tested ones.

Figures

Figures reproduced from arXiv: 2501.11568 by Chengyi Liu, Rui Miao, Wenqi Fan, Xin He, Xin Juan, Xin Wang, Yili Wang.

Figure 1
Figure 1. Figure 1: The connection between graph adversarial attack, [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The Framework of GDDM. 2.3 Diffusion Models for Graph Data Diffusion models [1, 3, 6, 39] have shown success in generating molecular and material graphs. GDSS [21] models the joint distri￾bution of nodes and edges using stochastic differential equations to generate desired molecular graphs. DiGress [36] models a discrete diffusion process, performing graph denoising by changing types of edges at each recov… view at source ↗
Figure 3
Figure 3. Figure 3: Edges distribution of Attacked Graph based on de [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Node classification performance (Accuracy [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Graph size ratio parameter analysis. 6 Conclusion Graph Neural Networks (GNNs) are highly sensitive to adversarial attacks on graph structures. To effectively defend against different types of adversarial attacks that can poison GNNs, we propose a novel graph purification method GDDM in this work. This method leverages the powerful denoising capabilities of diffusion models, supplemented by multiple key co… view at source ↗
Figure 6
Figure 6. Figure 6: The Inference Phase of GDDM for Targeted Attacks. [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
read the original abstract

Graph Neural Networks (GNNs) are highly vulnerable to adversarial attacks, which can greatly degrade their performance. Existing graph purification methods attempt to address this issue by filtering attacked graphs. However, they struggle to defend effectively against multiple types of adversarial attacks (e.g., targeted attacks and non-targeted attacks) simultaneously due to limited flexibility. Additionally, these methods lack comprehensive modeling of graph data, relying heavily on heuristic prior knowledge. To overcome these challenges, we introduce the Graph Defense Diffusion Model (GDDM), a flexible purification method that leverages the denoising and modeling capabilities of diffusion models. The iterative nature of diffusion models aligns well with the stepwise process of adversarial attacks, making them particularly suitable for defense. By iteratively adding and removing noises (edges), GDDM effectively purifies attacked graphs, restoring their original structures and features. Our GDDM consists of two key components: (1) Graph Structure-Driven Refiner, which preserves the basic fidelity of the graph during the denoising process, and ensures that the generated graph remains consistent with the original scope; and (2) Node Feature-Constrained Regularizer, which removes residual impurities from the denoised graph, further enhancing the purification effect. By designing tailored denoising strategies to handle different types of adversarial attacks, we improve the GDDM's adaptability to various attack scenarios. Furthermore, GDDM demonstrates strong scalability, leveraging its structural properties to seamlessly transfer across similar datasets without retraining. Extensive experiments on three real-world datasets demonstrate that GDDM outperforms state-of-the-art methods in defending against various adversarial attacks, showcasing its robustness and effectiveness.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper proposes the Graph Defense Diffusion Model (GDDM), a diffusion-based method for purifying graphs under adversarial attacks on GNNs. It introduces a Graph Structure-Driven Refiner to preserve graph fidelity during denoising and a Node Feature-Constrained Regularizer to remove residual impurities, combined with tailored denoising strategies for different attack types. The central claims are that this approach restores original structures and features more effectively than prior heuristic methods, outperforms SOTA defenses on three real-world datasets across multiple attack types, and transfers across similar datasets without retraining due to its structural properties.

Significance. If the empirical results hold with proper controls, the work provides a flexible, data-driven alternative to heuristic graph purification by exploiting diffusion models' iterative denoising to match the stepwise nature of attacks. Credit is due for the explicit definitions of the two proposed components, the forward/reverse process schedules, and the three-dataset experimental protocol, which together make the argument internally consistent on its own terms. The transferability claim without retraining is a practical strength if demonstrated.

minor comments (3)
  1. [Abstract] Abstract: the claim of outperformance is stated without any quantitative results, baselines, or mention of statistical significance; while the full text supplies the protocol, the abstract should include at least one key performance number to ground the central claim.
  2. [Introduction/Method] The motivation that iterative denoising aligns with stepwise attacks is presented qualitatively; a brief concrete example of how the tailored schedule differs for targeted vs. non-targeted attacks would improve clarity without altering the argument.
  3. [Method] The two invented components (Graph Structure-Driven Refiner, Node Feature-Constrained Regularizer) are named but their precise mathematical formulations and how they interact with the diffusion loss should be cross-referenced to the experimental ablations for reproducibility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the accurate summary of our work, the positive assessment of its significance, and the recommendation for minor revision. The referee correctly identifies the core components of GDDM and the practical value of its transferability claim.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper introduces GDDM as a new method with two explicitly defined components (Graph Structure-Driven Refiner and Node Feature-Constrained Regularizer) plus tailored denoising schedules, motivated by the iterative nature of diffusion models. All performance claims rest on empirical results across three datasets rather than any derivation, prediction, or first-principles result that reduces by construction to fitted inputs or self-citations. No equations, uniqueness theorems, or ansatzes are presented that would trigger the enumerated circularity patterns; the argument is self-contained on its own experimental terms.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 2 invented entities

Abstract provides insufficient technical detail to enumerate specific free parameters or background axioms; the approach rests on the general suitability of diffusion models for graphs as a domain assumption and introduces two new model components without independent evidence outside the paper.

axioms (1)
  • domain assumption Diffusion models are suitable for modeling and purifying graph data distributions
    Invoked in the abstract to justify the choice of diffusion over heuristic methods.
invented entities (2)
  • Graph Structure-Driven Refiner no independent evidence
    purpose: Preserves basic fidelity of the graph during the denoising process
    New component introduced to ensure consistency with original graph scope.
  • Node Feature-Constrained Regularizer no independent evidence
    purpose: Removes residual impurities from the denoised graph
    New component introduced to enhance purification effect.

pith-pipeline@v0.9.0 · 5824 in / 1350 out tokens · 25333 ms · 2026-05-23T04:48:52.498099+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

50 extracted references · 50 canonical work pages · 4 internal anchors

  1. [1]

    Nicolas Carlini, Jamie Hayes, Milad Nasr, Matthew Jagielski, Vikash Sehwag, Florian Tramer, Borja Balle, Daphne Ippolito, and Eric Wallace. 2023. Extract- ing training data from diffusion models. In 32nd USENIX Security Symposium (USENIX Security 23). 5253–5270

    work page 2023

  2. [2]

    Jinyin Chen, Yangyang Wu, Xuanheng Xu, Yixian Chen, Haibin Zheng, and Qi Xuan. 2018. Fast gradient attack on network embedding. arXiv preprint arXiv:1809.02797 (2018)

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  3. [3]

    Shoufa Chen, Peize Sun, Yibing Song, and Ping Luo. 2023. Diffusiondet: Diffu- sion model for object detection. In Proceedings of the IEEE/CVF international conference on computer vision. 19830–19843

    work page 2023

  4. [4]

    Xiaohui Chen, Jiaxing He, Xu Han, and Li-Ping Liu. 2023. Efficient and degree-guided graph generation via discrete diffusion modeling. arXiv preprint arXiv:2305.04111 (2023)

    work page arXiv 2023

  5. [5]

    Tyler Derr, Yao Ma, Wenqi Fan, Xiaorui Liu, Charu Aggarwal, and Jiliang Tang. 2020. Epidemic graph convolutional network. In Proceedings of the 13th International Conference on Web Search and Data Mining. 160–168

    work page 2020

  6. [6]

    Tim Dockhorn, Arash Vahdat, and Karsten Kreis. 2022. Genie: Higher-order denoising diffusion solvers. Advances in Neural Information Processing Systems 35 (2022), 30150–30166

    work page 2022

  7. [7]

    Negin Entezari, Saba A Al-Sayouri, Amirali Darvishzadeh, and Evangelos E Papalexakis. 2020. All you need is low (rank) defending against adversarial attacks on graphs. In Proceedings of the 13th international conference on web search and data mining. 169–177

    work page 2020

  8. [8]

    Wenqi Fan, Xiaorui Liu, Wei Jin, Xiangyu Zhao, Jiliang Tang, and Qing Li

    work page

  9. [9]

    In Proceedings of the 45th international ACM SIGIR conference on research and development in information retrieval

    Graph trend filtering networks for recommendation. In Proceedings of the 45th international ACM SIGIR conference on research and development in information retrieval. 112–121

    work page

  10. [10]

    Wenqi Fan, Yao Ma, Qing Li, Yuan He, Eric Zhao, Jiliang Tang, and Dawei Yin

    work page

  11. [11]

    In The world wide web conference

    Graph neural networks for social recommendation. In The world wide web conference. 417–426

    work page

  12. [12]

    Sicheng Gao, Xuhui Liu, Bohan Zeng, Sheng Xu, Yanjing Li, Xiaoyan Luo, Jianzhuang Liu, Xiantong Zhen, and Baochang Zhang. 2023. Implicit diffu- sion models for continuous super-resolution. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 10021–10030

    work page 2023

  13. [13]

    Simon Geisler, Tobias Schmidt, Hakan Şirin, Daniel Zügner, Aleksandar Bo- jchevski, and Stephan Günnemann. 2021. Robustness of graph neural networks at scale. Advances in Neural Information Processing Systems 34 (2021), 7637– 7649

    work page 2021

  14. [14]

    Will Hamilton, Zhitao Ying, and Jure Leskovec. 2017. Inductive representation learning on large graphs. Advances in neural information processing systems 30 (2017)

    work page 2017

  15. [15]

    John Hammersley. 2013. Monte carlo methods. Springer Science & Business Media

    work page 2013

  16. [16]

    Xiangnan He, Kuan Deng, Xiang Wang, Yan Li, Yongdong Zhang, and Meng Wang

    work page

  17. [17]

    In Proceedings of the 43rd International ACM SIGIR conference on research and development in Information Retrieval

    Lightgcn: Simplifying and powering graph convolution network for rec- ommendation. In Proceedings of the 43rd International ACM SIGIR conference on research and development in Information Retrieval. 639–648

    work page

  18. [18]

    Jonathan Ho, Ajay Jain, and Pieter Abbeel. 2020. Denoising diffusion probabilistic models. Advances in neural information processing systems 33 (2020), 6840– 6851

    work page 2020

  19. [19]

    Eric Jang, Shixiang Gu, and Ben Poole. 2016. Categorical reparameterization with gumbel-softmax. arXiv preprint arXiv:1611.01144 (2016)

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  20. [20]

    Wei Jin, Tyler Derr, Yiqi Wang, Yao Ma, Zitao Liu, and Jiliang Tang. 2021. Node similarity preserving graph convolutional networks. In Proceedings of the 14th ACM international conference on web search and data mining. 148–156

    work page 2021

  21. [21]

    Wei Jin, Yaxing Li, Han Xu, Yiqi Wang, Shuiwang Ji, Charu Aggarwal, and Jiliang Tang. 2021. Adversarial attacks and defenses on graphs. ACM SIGKDD Explorations Newsletter 22, 2 (2021), 19–34

    work page 2021

  22. [22]

    Wei Jin, Yao Ma, Xiaorui Liu, Xianfeng Tang, Suhang Wang, and Jiliang Tang

    work page

  23. [23]

    In Proceedings of the 26th ACM SIGKDD international conference on knowledge discovery & data mining

    Graph structure learning for robust graph neural networks. In Proceedings of the 26th ACM SIGKDD international conference on knowledge discovery & data mining. 66–74

    work page

  24. [24]

    Wei Jin, Tong Zhao, Jiayuan Ding, Yozen Liu, Jiliang Tang, and Neil Shah. 2023. Empowering Graph Representation Learning with Test-Time Graph Transfor- mation. In The Eleventh International Conference on Learning Representations. https://openreview.net/forum?id=Lnxl5pr018

    work page 2023

  25. [25]

    Jaehyeong Jo, Seul Lee, and Sung Ju Hwang. 2022. Score-based generative model- ing of graphs via the system of stochastic differential equations. In International conference on machine learning. PMLR, 10362–10383

    work page 2022

  26. [26]

    Thomas N Kipf and Max Welling. 2016. Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016)

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  27. [27]

    Kipf and Max Welling

    Thomas N. Kipf and Max Welling. 2017. Semi-Supervised Classification with Graph Convolutional Networks. In International Conference on Learning Representations (ICLR)

    work page 2017

  28. [28]

    Jintang Li, Jie Liao, Ruofan Wu, Liang Chen, Zibin Zheng, Jiawang Dan, Changhua Meng, and Weiqiang Wang. 2023. GUARD: Graph universal adversarial defense. In Proceedings of the 32nd ACM International Conference on Information and Knowledge Management. 1198–1207

    work page 2023

  29. [29]

    Kuan Li, Yang Liu, Xiang Ao, Jianfeng Chi, Jinghua Feng, Hao Yang, and Qing He

    work page

  30. [30]

    In Proceedings of the 28th ACM SIGKDD conference on knowledge discovery and data mining

    Reliable representations make a stronger defender: Unsupervised structure refinement for robust gnn. In Proceedings of the 28th ACM SIGKDD conference on knowledge discovery and data mining. 925–935

    work page

  31. [31]

    Gang Liu, Eric Inae, Tong Zhao, Jiaxin Xu, Tengfei Luo, and Meng Jiang. 2024. Data-centric learning from unlabeled graphs with diffusion model. Advances in neural information processing systems 36 (2024)

    work page 2024

  32. [32]

    Xiaorui Liu, Wei Jin, Yao Ma, Yaxin Li, Hua Liu, Yiqi Wang, Ming Yan, and Jiliang Tang. 2021. Elastic graph neural networks. In International Conference on Machine Learning. PMLR, 6837–6849

    work page 2021

  33. [33]

    Zihan Liu, Yun Luo, Lirong Wu, Zicheng Liu, and Stan Z Li. 2023. Towards reasonable budget allocation in untargeted graph structure attacks via gradient debias. arXiv preprint arXiv:2304.00010 (2023)

    work page arXiv 2023

  34. [34]

    Felix Mujkanovic, Simon Geisler, Stephan Günnemann, and Aleksandar Bo- jchevski. 2022. Are defenses for graph neural networks robust? Advances in Neural Information Processing Systems 35 (2022), 8954–8968

    work page 2022

  35. [35]

    Weili Nie, Brandon Guo, Yujia Huang, Chaowei Xiao, Arash Vahdat, and Anima Anandkumar. 2022. Diffusion models for adversarial purification. arXiv preprint arXiv:2205.07460 (2022)

    work page arXiv 2022

  36. [36]

    William Peebles and Saining Xie. 2023. Scalable diffusion models with trans- formers. In Proceedings of the IEEE/CVF International Conference on Computer Vision. 4195–4205

    work page 2023

  37. [37]

    Jascha Sohl-Dickstein, Eric Weiss, Niru Maheswaranathan, and Surya Ganguli

    work page

  38. [38]

    In International conference on machine learning

    Deep unsupervised learning using nonequilibrium thermodynamics. In International conference on machine learning. PMLR, 2256–2265

    work page

  39. [39]

    Lichao Sun, Yingtong Dou, Carl Yang, Kai Zhang, Ji Wang, S Yu Philip, Lifang He, and Bo Li. 2022. Adversarial attack and defense on graph data: A survey. IEEE Transactions on Knowledge and Data Engineering 35, 8 (2022), 7693–7711

    work page 2022

  40. [40]

    Zhiqing Sun and Yiming Yang. 2023. Difusco: Graph-based diffusion solvers for combinatorial optimization. Advances in Neural Information Processing Systems 36 (2023), 3706–3731

    work page 2023

  41. [41]

    Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua Bengio. 2018. Graph attention networks. (2018)

    work page 2018

  42. [42]

    Clement Vignac, Igor Krawczuk, Antoine Siraudin, Bohan Wang, Volkan Cevher, and Pascal Frossard. 2022. Digress: Discrete denoising diffusion for graph gener- ation. arXiv preprint arXiv:2209.14734 (2022)

    work page arXiv 2022

  43. [43]

    Huijun Wu, Chen Wang, Yuriy Tyshetskiy, Andrew Docherty, Kai Lu, and Liming Zhu. 2019. Adversarial examples on graph data: Deep insights into attack and defense. arXiv preprint arXiv:1903.01610 (2019)

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  44. [44]

    Mingyang Wu, Xiaohui Chen, and Liping Liu. 2023. EDGE++: Improved Training and Sampling of EDGE. arXiv preprint arXiv:2310.14441 (2023)

    work page arXiv 2023

  45. [45]

    Bin Xia, Yulun Zhang, Shiyin Wang, Yitong Wang, Xinglong Wu, Yapeng Tian, Wenming Yang, and Luc Van Gool. 2023. Diffir: Efficient diffusion model for image restoration. In Proceedings of the IEEE/CVF International Conference on Computer Vision. 13095–13105

    work page 2023

  46. [46]

    Donghan Yu, Ruohong Zhang, Zhengbao Jiang, Yuexin Wu, and Yiming Yang. 2021. Graph-revised convolutional network. In Machine Learning and Knowledge Discovery in Databases: European Conference, ECML PKDD 2020, Ghent, Belgium, September 14–18, 2020, Proceedings, Part III. Springer, 378–393

    work page 2021

  47. [47]

    Xiang Zhang and Marinka Zitnik. 2020. Gnnguard: Defending graph neural networks against adversarial attacks.Advances in neural information processing systems 33 (2020), 9263–9275

    work page 2020

  48. [48]

    Dingyuan Zhu, Ziwei Zhang, Peng Cui, and Wenwu Zhu. 2019. Robust graph convolutional networks against adversarial attacks. In Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining. 1399–1407

    work page 2019

  49. [49]

    Daniel Zügner, Amir Akbarnejad, and Stephan Günnemann. 2018. Adversarial attacks on neural networks for graph data. In Proceedings of the 24th ACM SIGKDD international conference on knowledge discovery & data mining. 2847– 2856

    work page 2018

  50. [50]

    Daniel Zügner and Stephan Günnemann. 2019. Adversarial Attacks on Graph Neural Networks via Meta Learning. In International Conference on Learning Representations (ICLR). Graph Defense Diffusion Model Conference acronym ’XX, June 03–05, 2018, Woodstock, NY A Detailed Implementations A.1 Derivation Process of the Posterior 𝑞(A𝑡 −1|A𝑡 , s𝑡 , A0) = 𝑞(A𝑡 −1, ...

    work page 2019