mlsanityData to 7 Oct 2026

Efficient and Degree-Guided Graph Generation via Discrete Diffusion Modeling

arXiv 2305.04111 ↗First posted 6 May 2023cs.LG cs.AI cs.SIcited by 75

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

Diffusion-based generative graph models have been proven effective in generating high-quality small graphs. However, they need to be more scalable for generating large graphs containing thousands of nodes desiring graph statistics. In this work, we propose EDGE, a new diffusion-based generative graph model that addresses generative tasks with large graphs. To improve computation efficiency, we encourage graph sparsity by using a discrete diffusion process that randomly removes edges at each time step and finally obtains an empty graph. EDGE only focuses on a portion of nodes in the graph at each denoising step. It makes much fewer edge predictions than previous diffusion-based models. Moreover, EDGE admits explicitly modeling the node degrees of the graphs, further improving the model performance. The empirical study shows that EDGE is much more efficient than competing methods and can generate large graphs with thousands of nodes. It also outperforms baseline models in generation quality: graphs generated by our approach have more similar graph statistics to those of the training graphs.

Key facts. Cited by 75 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 41 of its 61 references that are in the map. First posted on arXiv 6 May 2023.

Builds on

41 of 61 references.

Closest ancestors · 5

Same direction, newest first

  1. 2022NVDiff: Graph Generation through the Diffusion of Node Vectors19 Nov
  2. 2022Diffusion Models for Graphs Benefit From Discrete State Spaces4 Oct
  3. 2022DiGress: Discrete Denoising diffusion for graph generation29 Sep
  4. 2022Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations5 Feb
  5. 2020Permutation Invariant Graph Generation via Score-Based Generative Modeling2 Mar

Other references · 36

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  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  4. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
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  12. 2017Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learningcited by 935
24 more
  1. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 566
  2. 2020Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classificationcited by 500
  3. 2018GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Modelscited by 406
  4. 2018GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoderscited by 375
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  6. 2019Efficient Graph Generation with Graph Recurrent Attention Networkscited by 231
  7. 2018Learning Deep Generative Models of Graphscited by 227
  8. 2018Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discoverycited by 191
  9. 2020MoFlow: An Invertible Flow Model for Generating Molecular Graphscited by 183
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  12. 2020A Survey on The Expressive Power of Graph Neural Networkscited by 111
  13. 2019Graph Normalizing Flowscited by 103
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  16. 2020Dirichlet Graph Variational Autoencodercited by 40
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  19. 2021Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutionscited by 38
  20. 2020Categorical Normalizing Flows via Continuous Transformationscited by 36
  21. 2020The impossibility of low rank representations for triangle-rich complex networkscited by 32
  22. 2021Order Matters: Probabilistic Modeling of Node Sequence for Graph Generationcited by 32
  23. 2021On the Power of Edge Independent Graph Modelscited by 13
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 10; 2024: 23; 2025: 24; 2026: 18.

75 papers.

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By area:

  1. 2024Discrete-state Continuous-time Diffusion for Graph Generationcited by 73
  2. 2023Enhancing Deep Reinforcement Learning: A Tutorial on Generative Diffusion Models in Network Optimizationcited by 56
  3. 2023Efficient and Scalable Graph Generation through Iterative Local Expansioncited by 35
  4. 2024Cometh: A continuous-time discrete-state graph diffusion modelcited by 29
  5. 2025DiffMS: Diffusion Generation of Molecules Conditioned on Mass Spectracited by 28
  6. 2023Sparse Training of Discrete Diffusion Models for Graph Generationcited by 26
  7. 2023Data-centric Graph Learning: A Surveycited by 22
  8. 2024Optimizing OOD Detection in Molecular Graphs: A Novel Approach with Diffusion Modelscited by 21
  9. 2024Hyperbolic Geometric Latent Diffusion Model for Graph Generationcited by 20
  10. 2024Generative Modelling of Structurally Constrained Graphscited by 17
  11. 2025Graph Generative Pre-trained Transformercited by 16
  12. 2025MADGEN: Mass-Spec attends to De Novo Molecular generationcited by 16
38 more
  1. 2023GraphMaker: Can Diffusion Models Generate Large Attributed Graphs?cited by 15
  2. 2024Advancing Graph Generation through Beta Diffusioncited by 13
  3. 2025Flatten Graphs as Sequences: Transformers are Scalable Graph Generatorscited by 12
  4. 2025Simple and Critical Iterative Denoising: A Recasting of Discrete Diffusion in Graph Generationcited by 9
  5. 2024Cross-Domain Graph Data Scaling: A Showcase with Diffusion Modelscited by 8
  6. 2024HYGENE: A Diffusion-based Hypergraph Generation Methodcited by 8
  7. 2024LayerDAG: A Layerwise Autoregressive Diffusion Model for Directed Acyclic Graph Generationcited by 8
  8. 2025Bures-Wasserstein Flow Matching for Graph Generationcited by 7
  9. 2024Reviving Life on the Edge: Joint Score-Based Graph Generation of Rich Edge Attributescited by 6
  10. 2024FairWire: Fair Graph Generationcited by 6
  11. 2023HiGen: Hierarchical Graph Generative Networkscited by 5
  12. 2024Neural Graph Generator: Feature-Conditioned Graph Generation using Latent Diffusion Modelscited by 5
  13. 2024How Fair is Your Diffusion Recommender Model?cited by 5
  14. 2025FragFM: Hierarchical Framework for Efficient Molecule Generation via Fragment-Level Discrete Flow Matchingcited by 5
  15. 2025Graph Guided Diffusion: Unified Guidance for Conditional Graph Generationcited by 5
  16. 2025PowerGrow: Feasible Co-Growth of Structures and Dynamics for Power Grid Synthesiscited by 5
  17. 2026Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generationcited by 5
  18. 2026RADAR: Redundancy-Aware Diffusion for Multi-Agent Communication Structure Generationcited by 5
  19. 2024Diffusion Twigs with Loop Guidance for Conditional Graph Generationcited by 4
  20. 2024FAP-CD: Fairness-Driven Age-Friendly Community Planning via Conditional Diffusion Generationcited by 4
  21. 2023EDGE++: Improved Training and Sampling of EDGEcited by 3
  22. 2024TDNetGen: Empowering Complex Network Resilience Prediction with Generative Augmentation of Topology and Dynamicscited by 3
  23. 2025Diffusion Models in Recommendation Systems: A Surveycited by 3
  24. 2025Graph Defense Diffusion Modelcited by 3
  25. 2025Backdoor Attacks on Discrete Graph Diffusion Modelscited by 3
  26. 2025A Non-Asymptotic Convergent Analysis for Scored-Based Graph Generative Model via a System of Stochastic Differential Equationscited by 3
  27. 2023Graph Generation with K2-treescited by 2
  28. 2023CDGraph: Dual Conditional Social Graph Synthesizing via Diffusion Modelcited by 2
  29. 2024Diffusion-based Graph Generative Methodscited by 2
  30. 2024Large Generative Graph Modelscited by 2
  31. 2024Random Walk Diffusion for Efficient Large-Scale Graph Generationcited by 2
  32. 2024EDGE-Rec: Efficient and Data-Guided Edge Diffusion For Recommender Systems Graphscited by 2
  33. 2025Graph Representation Learning with Diffusion Generative Modelscited by 2
  34. 2025Fast Graph Generation via Autoregressive Noisy Filtration Modelingcited by 2
  35. 2025GDGB: A Benchmark for Generative Dynamic Text-Attributed Graph Learningcited by 2
  36. 2025SBGD: Improving Graph Diffusion Generative Model via Stochastic Block Diffusioncited by 2
  37. 2026Flowette: Flow Matching with Graphette Priors for Graph Generationcited by 2
  38. 2026Unrestrained Simplex Denoising for Discrete Data. A Non-Markovian Approach Applied to Graph Generationcited by 2

50 most cited of 75 All 75 (JSON)

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  3. 2023Generative Diffusion Models on Graphs: Methods and Applications
  4. 2023Graph Generation with Diffusion Mixture
  5. 2024IFH: a Diffusion Framework for Flexible Design of Graph Generative Models
  6. 2022Fast Graph Generation via Spectral Diffusion
  7. 2025Diffusion-Free Graph Generation with Next-Scale Prediction
  8. 2024Unifying Generation and Prediction on Graphs with Latent Graph Diffusion