mlsanityData to 7 Oct 2026

DiGress: Discrete Denoising diffusion for graph generation

arXiv 2209.14734 ↗First posted 29 Sep 2022cs.LGcited by 503

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

Abstract (arXiv)

This work introduces DiGress, a discrete denoising diffusion model for generating graphs with categorical node and edge attributes. Our model utilizes a discrete diffusion process that progressively edits graphs with noise, through the process of adding or removing edges and changing the categories. A graph transformer network is trained to revert this process, simplifying the problem of distribution learning over graphs into a sequence of node and edge classification tasks. We further improve sample quality by introducing a Markovian noise model that preserves the marginal distribution of node and edge types during diffusion, and by incorporating auxiliary graph-theoretic features. A procedure for conditioning the generation on graph-level features is also proposed. DiGress achieves state-of-the-art performance on molecular and non-molecular datasets, with up to 3x validity improvement on a planar graph dataset. It is also the first model to scale to the large GuacaMol dataset containing 1.3M drug-like molecules without the use of molecule-specific representations.

Key facts. Cited by 503 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 48 of its 62 references that are in the map. First posted on arXiv 29 Sep 2022.

Builds on

48 of 62 references.

Closest ancestors · 5

Same direction, newest first

  1. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem8 Jun
  2. 2022Equivariant Diffusion for Molecule Generation in 3D31 Mar
  3. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation6 Mar
  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 · 43

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  4. 2018How Powerful are Graph Neural Networks?cited by 4,355
  5. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  6. 2017FiLM: Visual Reasoning with a General Conditioning Layercited by 2,286
  7. 2022Video Diffusion Modelscited by 2,280
  8. 2015Variational Inference with Normalizing Flowscited by 2,161
  9. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  10. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,419
  11. 2021Variational Diffusion Modelscited by 1,145
  12. 2017MoleculeNet: A Benchmark for Molecular Machine Learningcited by 1,037
31 more
  1. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 878
  2. 2020A Generalization of Transformer Networks to Graphscited by 653
  3. 2018Junction Tree Variational Autoencoder for Molecular Graph Generationcited by 647
  4. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 566
  5. 2022A Continuous Time Framework for Discrete Denoising Modelscited by 437
  6. 2018GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Modelscited by 406
  7. 2019Provably Powerful Graph Networkscited by 385
  8. 2020Improving Graph Neural Network Expressivity via Subgraph Isomorphism Countingcited by 312
  9. 2018GuacaMol: Benchmarking Models for De Novo Molecular Designcited by 294
  10. 2018Molecular Sets (MOSES): A Benchmarking Platform for Molecular Generation Modelscited by 270
  11. 2022Torsional Diffusion for Molecular Conformer Generationcited by 262
  12. 2022Diffsound: Discrete Diffusion Model for Text-to-sound Generationcited by 256
  13. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 248
  14. 2020Can Graph Neural Networks Count Substructures?cited by 235
  15. 2019Efficient Graph Generation with Graph Recurrent Attention Networkscited by 231
  16. 2020Hierarchical Generation of Molecular Graphs using Structural Motifscited by 204
  17. 2020MoFlow: An Invertible Flow Model for Generating Molecular Graphscited by 183
  18. 2018Constrained Graph Variational Autoencoders for Molecule Designcited by 182
  19. 2021GraphDF: A Discrete Flow Model for Molecular Graph Generationcited by 177
  20. 2020Directional Graph Networkscited by 132
  21. 2019GraphNVP: An Invertible Flow Model for Generating Molecular Graphscited by 115
  22. 2022SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generatorscited by 96
  23. 2020Building powerful and equivariant graph neural networks with structural message-passingcited by 95
  24. 2021Learning to Extend Molecular Scaffolds with Structural Motifscited by 70
  25. 2022A Survey on Deep Graph Generation: Methods and Applicationscited by 69
  26. 2018Generative Code Modeling with Graphscited by 59
  27. 2022SpeqNets: Sparsity-aware Permutation-equivariant Graph Networkscited by 37
  28. 2020Categorical Normalizing Flows via Continuous Transformationscited by 36
  29. 2021Top-N: Equivariant set and graph generation without exchangeabilitycited by 36
  30. 2022SizeShiftReg: a Regularization Method for Improving Size-Generalization in Graph Neural Networkscited by 36
  31. 2021Beyond In-Place Corruption: Insertion and Deletion In Denoising Probabilistic Modelscited by 23

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 88; 2024: 138; 2025: 138; 2026: 136.

503 papers.

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  1. 2024Simple and Effective Masked Diffusion Language Modelscited by 800
  2. 2024Simplified and Generalized Masked Diffusion for Discrete Datacited by 606
  3. 2024Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Designcited by 294
  4. 2023Self-Consuming Generative Models Go MADcited by 239
  5. 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimizationcited by 216
  6. 2023Large Language Models on Graphs: A Comprehensive Surveycited by 190
  7. 2023Protein Design with Guided Discrete Diffusioncited by 154
  8. 2023A Reparameterized Discrete Diffusion Model for Text Generationcited by 152
  9. 2024Simple Guidance Mechanisms for Discrete Diffusion Modelscited by 148
  10. 2023Crystal Structure Prediction by Joint Equivariant Diffusioncited by 142
  11. 2024Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decodingcited by 127
  12. 2024Unlocking Guidance for Discrete State-Space Diffusion and Flow Modelscited by 124
38 more
  1. 2023On Memorization in Diffusion Modelscited by 122
  2. 2022Equivariant 3D-Conditional Diffusion Models for Molecular Linker Designcited by 121
  3. 2024InstructScene: Instruction-Driven 3D Indoor Scene Synthesis with Semantic Graph Priorcited by 110
  4. 2024Dirichlet Flow Matching with Applications to DNA Sequence Designcited by 110
  5. 2023MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generationcited by 96
  6. 2024DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Designcited by 87
  7. 2023A Complete Survey on Generative AI (AIGC): Is ChatGPT from GPT-4 to GPT-5 All You Need?cited by 84
  8. 2024Position: Graph Foundation Models are Already Herecited by 84
  9. 2023Autoregressive Diffusion Model for Graph Generationcited by 82
  10. 2023Diffusion-Based 3D Human Pose Estimation with Multi-Hypothesis Aggregationcited by 81
  11. 2023Generative Diffusion Models on Graphs: Methods and Applicationscited by 79
  12. 2024Variational Flow Matching for Graph Generationcited by 78
  13. 2023Efficient and Degree-Guided Graph Generation via Discrete Diffusion Modelingcited by 75
  14. 2024Discrete-state Continuous-time Diffusion for Graph Generationcited by 73
  15. 2022Diffusion Models for Graphs Benefit From Discrete State Spacescited by 69
  16. 2023PolyDiff: Generating 3D Polygonal Meshes with Diffusion Modelscited by 66
  17. 2024EchoScene: Indoor Scene Generation via Information Echo over Scene Graph Diffusioncited by 66
  18. 2023MolDiff: Addressing the Atom-Bond Inconsistency Problem in 3D Molecule Diffusion Generationcited by 65
  19. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  20. 2024Many Heads Are Better Than One: Improved Scientific Idea Generation by A LLM-Based Multi-Agent Systemcited by 63
  21. 2024TabDiff: a Mixed-type Diffusion Model for Tabular Data Generationcited by 60
  22. 2024Informed Correctors for Discrete Diffusion Modelscited by 57
  23. 2023Enhancing Deep Reinforcement Learning: A Tutorial on Generative Diffusion Models in Network Optimizationcited by 56
  24. 2023Graph Metanetworks for Processing Diverse Neural Architecturescited by 55
  25. 2023Improving 3D Imaging with Pre-Trained Perpendicular 2D Diffusion Modelscited by 53
  26. 2024Discrete Copula Diffusioncited by 53
  27. 2023Graph Generation with Diffusion Mixturecited by 52
  28. 2023Scalable Diffusion for Materials Generationcited by 52
  29. 2024Feedback Efficient Online Fine-Tuning of Diffusion Modelscited by 52
  30. 2025Position: Graph Learning Will Lose Relevance Due To Poor Benchmarkscited by 52
  31. 2024How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Frameworkcited by 48
  32. 2025SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Modelscited by 48
  33. 2025GenMol: A Drug Discovery Generalist with Discrete Diffusioncited by 47
  34. 2025Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithmscited by 47
  35. 2025Theoretical Benefit and Limitation of Diffusion Language Modelcited by 46
  36. 2023Graph Denoising Diffusion for Inverse Protein Foldingcited by 44
  37. 2024Graph Diffusion Transformers for Multi-Conditional Molecular Generationcited by 44
  38. 2023MUDiff: Unified Diffusion for Complete Molecule Generationcited by 41

50 most cited of 503 All 503 (JSON)

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  1. 2026Efficient Graph Generation via Direct Prediction and Flow Matching
  2. 2023Conditional Diffusion Based on Discrete Graph Structures for Molecular Graph Generation
  3. 2025Graffe: Graph Representation Learning via Diffusion Probabilistic Models
  4. 2025DiffGraph: Heterogeneous Graph Diffusion Model
  5. 2023Directional diffusion models for graph representation learning
  6. 2026Discrete Diffusion for Large Graph Generation via Structural Candidate Restriction
  7. 2024SubGDiff: A Subgraph Diffusion Model to Improve Molecular Representation Learning
  8. 2024DeFoG: Discrete Flow Matching for Graph Generation