mlsanityData to 14 Oct 2026

Diffusion Models for Graphs Benefit From Discrete State Spaces

arXiv 2210.01549 ↗First posted 4 Oct 2022cs.LG cs.SI stat.MLcited by 73

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

Abstract (arXiv)

Denoising diffusion probabilistic models and score-matching models have proven to be very powerful for generative tasks. While these approaches have also been applied to the generation of discrete graphs, they have, so far, relied on continuous Gaussian perturbations. Instead, in this work, we suggest using discrete noise for the forward Markov process. This ensures that in every intermediate step the graph remains discrete. Compared to the previous approach, our experimental results on four datasets and multiple architectures show that using a discrete noising process results in higher quality generated samples indicated with an average MMDs reduced by a factor of 1.5. Furthermore, the number of denoising steps is reduced from 1000 to 32 steps, leading to a 30 times faster sampling procedure.

Key facts. Cited by 73 papers in the map (data through 14 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 26 of its 35 references that are in the map. First posted on arXiv 4 Oct 2022.

Builds on

26 of 35 references.

Closest ancestors · 3

Same direction, newest first

  1. 2022DiGress: Discrete Denoising diffusion for graph generation29 Sep
  2. 2022Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations5 Feb
  3. 2020Permutation Invariant Graph Generation via Score-Based Generative Modeling2 Mar

Other references · 23

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2020Denoising Diffusion Implicit Modelscited by 9,781
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  5. 2022Generative Adversarial Networkscited by 5,627
  6. 2018How Powerful are Graph Neural Networks?cited by 4,393
  7. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  8. 2013Auto-Encoding Variational Bayescited by 4,053
  9. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
  10. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,719
  11. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 574
  12. 2018GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Modelscited by 413
11 more
  1. 2018MolGAN: An implicit generative model for small molecular graphscited by 393
  2. 2019Provably Powerful Graph Networkscited by 389
  3. 2018GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoderscited by 383
  4. 2019Efficient Graph Generation with Graph Recurrent Attention Networkscited by 234
  5. 2021Autoregressive Diffusion Modelscited by 210
  6. 2021ImageBART: Bidirectional Context with Multinomial Diffusion for Autoregressive Image Synthesiscited by 122
  7. 2019Graph Normalizing Flowscited by 104
  8. 2022SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generatorscited by 99
  9. 2021Unleashing Transformers: Parallel Token Prediction with Discrete Absorbing Diffusion for Fast High-Resolution Image Generation from Vector-Quantized Codescited by 71
  10. 2021Top-N: Equivariant set and graph generation without exchangeabilitycited by 36
  11. 2016Graphons, mergeons, and so on!cited by 10

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 19; 2024: 20; 2025: 15; 2026: 19.

73 papers.

Sort:

By area:

  1. 2023A Reparameterized Discrete Diffusion Model for Text Generationcited by 152
  2. 2023MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generationcited by 98
  3. 2023A Complete Survey on Generative AI (AIGC): Is ChatGPT from GPT-4 to GPT-5 All You Need?cited by 84
  4. 2023Autoregressive Diffusion Model for Graph Generationcited by 83
  5. 2023Generative Diffusion Models on Graphs: Methods and Applicationscited by 81
  6. 2023Efficient and Degree-Guided Graph Generation via Discrete Diffusion Modelingcited by 80
  7. 2024Discrete-state Continuous-time Diffusion for Graph Generationcited by 76
  8. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 66
  9. 2023MolDiff: Addressing the Atom-Bond Inconsistency Problem in 3D Molecule Diffusion Generationcited by 65
  10. 2025Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithmscited by 47
  11. 2023AbDiffuser: Full-Atom Generation of in vitro Functioning Antibodiescited by 35
  12. 2024Cometh: A continuous-time discrete-state graph diffusion modelcited by 32
38 more
  1. 2023Sparse Training of Discrete Diffusion Models for Graph Generationcited by 27
  2. 2024Diffusion Models in textitDe Novo Drug Designcited by 26
  3. 2024Unifying Generation and Prediction on Graphs with Latent Graph Diffusioncited by 25
  4. 2024Generative Modelling of Structurally Constrained Graphscited by 19
  5. 2025Graph Generative Pre-trained Transformercited by 17
  6. 2023Directional diffusion models for graph representation learningcited by 13
  7. 2023SaGess: Sampling Graph Denoising Diffusion Model for Scalable Graph Generationcited by 13
  8. 2024Advancing Graph Generation through Beta Diffusioncited by 13
  9. 2025Simple and Critical Iterative Denoising: A Recasting of Discrete Diffusion in Graph Generationcited by 10
  10. 2023Complexity-aware Large Scale Origin-Destination Network Generation via Diffusion Modelcited by 9
  11. 2023D4Explainer: In-Distribution GNN Explanations via Discrete Denoising Diffusioncited by 9
  12. 2024A Directional Diffusion Graph Transformer for Recommendationcited by 9
  13. 20243D Vessel Graph Generation Using Denoising Diffusioncited by 9
  14. 2025Bures-Wasserstein Flow Matching for Graph Generationcited by 9
  15. 2024Generating Graphs via Spectral Diffusioncited by 8
  16. 2024Cross-Domain Graph Data Scaling: A Showcase with Diffusion Modelscited by 8
  17. 2023HiGen: Hierarchical Graph Generative Networkscited by 6
  18. 2024Reviving Life on the Edge: Joint Score-Based Graph Generation of Rich Edge Attributescited by 6
  19. 2023Generative Explanations for Graph Neural Network: Methods and Evaluationscited by 4
  20. 2024SubGDiff: A Subgraph Diffusion Model to Improve Molecular Representation Learningcited by 4
  21. 2024FAP-CD: Fairness-Driven Age-Friendly Community Planning via Conditional Diffusion Generationcited by 4
  22. 2025Diffusion on Graph: Augmentation of Graph Structure for Node Classificationcited by 4
  23. 2025Topological Schr"odinger Bridge Matchingcited by 4
  24. 2026Learning Structure-Semantic Evolution Trajectories for Graph Domain Adaptationcited by 4
  25. 2023EDGE++: Improved Training and Sampling of EDGEcited by 3
  26. 2024Random Walk Diffusion for Efficient Large-Scale Graph Generationcited by 3
  27. 2025Do Graph Diffusion Models Accurately Capture and Generate Substructure Distributions?cited by 3
  28. 2025Generating Directed Graphs with Dual Attention and Asymmetric Encodingcited by 3
  29. 2026Flowette: Flow Matching with Graphette Priors for Graph Generationcited by 3
  30. 2023Tertiary Lymphoid Structures Generation through Graph-based Diffusioncited by 2
  31. 2023On the Inherent Privacy Properties of Discrete Denoising Diffusion Modelscited by 2
  32. 2024Latent Conditional Diffusion-based Data Augmentation for Continuous-Time Dynamic Graph Modelcited by 2
  33. 2025DiffGED: Computing Graph Edit Distance via Diffusion-based Graph Matchingcited by 2
  34. 2025Satellites Reveal Mobility: A Commuting Origin-destination Flow Generator for Global Citiescited by 2
  35. 2025LGDC: Latent Graph Diffusion via Spectrum-Preserving Coarseningcited by 2
  36. 2026Inference Attacks Against Graph Generative Diffusion Modelscited by 2
  37. 2026Unrestrained Simplex Denoising for Discrete Data. A Non-Markovian Approach Applied to Graph Generationcited by 2
  38. 2026Hierarchical Discrete Flow Matching for Graph Generationcited by 2

50 most cited of 73 All 73 (JSON)

Similar, not cited

Close in wording, no citation either way

  1. 2024Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformization
  2. 2025Bit-Level Discrete Diffusion with Markov Probabilistic Models: An Improved Framework with Sharp Convergence Bounds under Minimal Assumptions
  3. 2024Unified Discrete Diffusion for Categorical Data
  4. 2023Complex Preferences for Different Convergent Priors in Discrete Graph Diffusion
  5. 2022From Denoising Diffusions to Denoising Markov Models
  6. 2024Diffusion-based Graph Generative Methods
  7. 2026Learning Discrete Diffusion of Graphs via Free-Energy Gradient Flows
  8. 2025Discrete State Diffusion Models: A Sample Complexity Perspective