Title: Topology-aware Graph Diffusion Model with Persistent Homology
Venue: NeurIPS 2025
Accepted: yes
Keywords: Graph Generation

Diffusion

Topology

Brain Network
Abstract: Generating realistic graphs faces challenges in estimating accurate distribution of graphs in an embedding space while preserving structural characteristics. However, existing graph generation methods primarily focus on approximating the joint distribution of nodes and edges, often overlooking topological properties such as connected components and loops, hindering accurate representation of global structures. To address this issue, we propose a Topology-Aware diffusion-based Graph Generation (TAGG), which aims to sample synthetic graphs that closely resemble the structural characteristics of the original graph based on persistent homology. Specifically, we suggest two core components: 1) Persistence Diagram Matching (PDM) loss which ensures high topological fidelity of generated graphs, and 2) topology-aware attention module (TAM) which induces the denoising network to capture the homological characteristics of the original graphs. Extensive experiments on conventional graph benchmarks demonstrate the effectiveness of our approach demonstrating high generation performance across various metrics, while achieving closer alignment with the distribution of topological features observed in the original graphs. Furthermore, application to real brain network data showcases its potential for complex and real graph applications.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis manuscript introduces a method to integrate persistent homology into graph diffusion models. The approach comprises three steps: (1) compute the persistence landscape from input graphs; (2) embed the landscape into the diffusion backbone via an attention module; and (3) augment the base diffusion loss (as in [38]) with an additional term comparing persistence diagrams.\n\nSTRENGTHS AND WEAKNESSES:\nThe overall idea of incorporating global information of a graph into the generative model is nice. The proposed method of using the persistence landscape might be a good way to do so. The presentation is clear and easy to follow and the problem is important in the context of graph generative models.\n\nHowever, the idea of using persistence diagrams in graph models is not new. For example, this work [1] already explored the idea of using persistence diagrams in message passing neural networks. I understand that the authors are using a different approach by combining the persistence landscape with an attention module, but there is no justification of why this is better than using persistence image + message passing as done in [1]. I think at least some empirical comparison is needed to justify the proposed method. \n\n[1] Zhao et al. 2020, Persistence Enhanced Graph Neural Network, AISTATS\n\nQUESTIONS:\n1. The loss in Equation (11) involves an optimization subproblem. How do you compute gradients through this inner optimization during backpropagation?\n2. In Line 103, you describe “adding the node $v_1$,” but multiple nodes may be added simultaneously. Could you clarify this step in the algorithm?\n3. In Section 5.4, TAGG’s superior homology preservation is expected by design. Can you perform an ablation study that adds only the persistence-loss term to other baseline models to disentangle the contributions of topology loss and attention fusion?\n\nLIMITATIONS:\nBesides the limitations pointed out by the authors, I'd like to bring up one another possible limitation: the computation of persistence diagrams seem to limited to graphs with small sizes and maybe this is worth pointing out in the paper.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper presents TAGG, a topology-aware graph generation framework that integrates persistent homology into diffusion models to better account for topological/structural information of undirected graphs. In particular, the authors introduce a novel loss function ( persistence diagram matching PDM), which enforces topological similarity between generated and original graphs, and a topology-aware attention mechanism that augments the self-attention module with homological features. The proposed approach is evaluated across four datasets (two synthetic ones), including brain networks.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths \n\n- The paper is well-written and clear;\n- The application on brain networks is very interesting with many nice visualizations;\n- The authors provide ablation studies to validate the effectiveness of their loss function and topology-aware attention mechanism.\n\nWeaknesses\n\n**Novelty**. I consider the novelty limited as:\n\n- The core generation process closely follows the method in [1];\n- Topology-aware loss functions based on PH have been abundant in graph representation learning [e.g., 2,3];\n- TAM consists of a minor modification of a standard self-attention module, incorporating topological features.\n\n[1] Digress: Discrete denoising diffusion for graph generation. ICLR, 2023. \n\n[2] Improving Self-supervised Molecular Representation Learning using Persistent Homology. NeurIPS, 2023.\n\n[3] Boosting Graph Pooling with Persistent Homology. NeurIPS, 2024.\n\n**Experiments**. I have concerns regarding the completeness and significance of the experiments. In particular:\n- The paper says it \"performed three replicate experiments to report averaged performance\". Could you report the variances?\n- Important evaluation metrics are missing, such as novelty & uniqueness or spectrum (see [4] for others).\n- Also, the paper lacks baselines for one-shot graph generation, such as SPECTRE [4].\n- Overall, this paper would benefit from considering more datasets. I would like to see more results on molecular graphs, and assess how the proposal compares with SOTA for molecule generation (e.g., see [1]).\n\n[4] SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators. ICML, 2022.\n\n**Motivation**. Overall, modeling graph distributions requires capturing a diverse range of structural patterns. I am not entirely convinced that better accounting for homological features (btw, I believe the paper refers to persistent (detailed) homological features) would lead to better models in general, considering the diversity of structural patterns. This is more pronounced because the topological information in the proposal is derived from a fixed filtration and a specific choice of vectorization. These design choices are not adequately motivated. In addition, only the average topological embedding (from training) is used --- it is unclear to me why such a simple modeling choice would work across different graph distributions.\n\nQUESTIONS:\n1. Regarding homological similarity, could you report the distributions of betti_0 and betti_1 for the generated graphs from different models and test data? \n2. How does the choice of vectorization and filtration function impact the overall performance? The method should work for any choice of vectorization, no?! What is the motivation for persistence landscapes?\n3. Does the incorporation of $\\mu_{G_0}$ in the attention layer lead to a constant additive term in Eq. (9) across all diffusion steps? \n4. Could the authors report results with random $\\mu_{G_0}$? I would like to know the sensitivity to that choice.\n5. How does the proposed model compare with Digress on their evaluation setup?\n6. In line 112, what if the homological feature does not disappear?\n\nLIMITATIONS:\nThe paper briefly discusses limitations in Section 6.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-02"}

comments: SUMMARY:
Classical methods for operations on graphs, such as random graph generation or graph denoising, sometimes scramble important graph features that we need. One of these features is the topology of the graph. The paper does a good job addressing this problem.

STRENGTHS AND WEAKNESSES:
The paper is well written and seems to make an important contribution.

QUESTIONS:
Can these methods be generalized to general simplicial complexes rather than just graphs?

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 4
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-02

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors introduce a graph generation method based on discrete diffusion, defined as topology-aware because it also preserves the structural features of the original graphs. The approach uses a loss function based on Persistence Diagram Matching (PDM) and integrates a Topology-aware Attention Module within the denoising network.\nSeveral experiments are presented, with a focus on the application to complex brain network data, showing the method’s effectiveness in real-world scenarios.\n\nSTRENGTHS AND WEAKNESSES:\n*Strengths*\n- The issue of reconstructing the homological features of the original graphs is very important, and the proposed method is therefore interesting because it explicitly addresses this aspect. The experiments on homological assessment are also very interesting.\n\n*Weaknesses*\n\n- Persistent homology works better and makes more sense on graphs that are not small. The experiments on Ego-Small are therefore particularly challenging and appreciated. However, I would have included, at least in the appendix, experiments on standard datasets such as SBM and Planar. I expect the model to achieve performance at least on par with other methods on these datasets.\n- The computational cost analysis is done in comparison with DiGress, which is known to be a discrete diffusion method and relatively slow. To have a more informative comparison, I suggest including at least one continuous diffusion method. This point should also be stressed in the limitations.\n- Persistent homology is always a difficult topic, and since it is allowed, I would add in the appendix a richer explanation in terms of graphical support for Section 3 (Preliminaries), to help readers who are less familiar with topology.\n- The experiments are missing standard metrics such as Validity, Novelty, and Uniqueness, which are common in graph generation works. Even if they are not directly related to topology, they are useful to provide a more complete picture of the generative model’s capabilities.\n- In the sentence \n>“Recently, diffusion-based methods [3, 20, 38] showed promising capability in graph generation, by defining the forward and reverse diffusion processes and training a neural network that mimics the reverse process to reconstruct the graphs.”\n\nI suggest adding two recent references that propose methods based on diffusion in the graph spectrum, which also capture both local and global structural information:\n\n- Martinkus, K., Loukas, A., Perraudin, N., & Wattenhofer, R. (2022, June). Spectre: Spectral conditioning helps to overcome the expressivity limits of one-shot graph generators. In ICML.\n- Minello, G., Bicciato, A., Rossi, L., Torsello, A., & Cosmo, L. (2025). Generating graphs via spectral diffusion. In ICLR.\n\nQUESTIONS:\nPlease see above\n\nLIMITATIONS:\nMissing runtime analysis", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-05"}