mlsanityData to 7 Oct 2026

Permutation Invariant Graph Generation via Score-Based Generative Modeling

arXiv 2003.00638 ↗First posted 2 Mar 2020cs.LG stat.MLcited by 263

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

Abstract (arXiv)

Learning generative models for graph-structured data is challenging because graphs are discrete, combinatorial, and the underlying data distribution is invariant to the ordering of nodes. However, most of the existing generative models for graphs are not invariant to the chosen ordering, which might lead to an undesirable bias in the learned distribution. To address this difficulty, we propose a permutation invariant approach to modeling graphs, using the recent framework of score-based generative modeling. In particular, we design a permutation equivariant, multi-channel graph neural network to model the gradient of the data distribution at the input graph (a.k.a., the score function). This permutation equivariant model of gradients implicitly defines a permutation invariant distribution for graphs. We train this graph neural network with score matching and sample from it with annealed Langevin dynamics. In our experiments, we first demonstrate the capacity of this new architecture in learning discrete graph algorithms. For graph generation, we find that our learning approach achieves better or comparable results to existing models on benchmark datasets.

Key facts. Cited by 263 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 27 of its 45 references that are in the map. First posted on arXiv 2 Mar 2020.

Builds on

27 of 45 references.

References · 27

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  4. 2017Graph Attention Networkscited by 8,854
  5. 2017Inductive Representation Learning on Large Graphscited by 6,284
  6. 2018How Powerful are Graph Neural Networks?cited by 4,355
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  9. 2016Density estimation using Real NVPcited by 2,029
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  12. 2016Automatic chemical design using a data-driven continuous representation of moleculescited by 762
15 more
  1. 2015Convolutional Networks on Graphs for Learning Molecular Fingerprintscited by 751
  2. 2018Junction Tree Variational Autoencoder for Molecular Graph Generationcited by 647
  3. 2018GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Modelscited by 406
  4. 2018GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoderscited by 375
  5. 2018Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generationcited by 363
  6. 2018Neural Relational Inference for Interacting Systemscited by 339
  7. 2018Learning Deep Generative Models of Graphscited by 227
  8. 2019Universal Invariant and Equivariant Graph Neural Networkscited by 182
  9. 2019GraphNVP: An Invertible Flow Model for Generating Molecular Graphscited by 115
  10. 2018Graphite: Iterative Generative Modeling of Graphscited by 112
  11. 2019Exploring Randomly Wired Neural Networks for Image Recognitioncited by 103
  12. 2019Graph Normalizing Flowscited by 103
  13. 2017Knowledge Transfer for Out-of-Knowledge-Base Entities: A Graph Neural Network Approachcited by 102
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 18; 2022: 31; 2023: 51; 2024: 69; 2025: 58; 2026: 36.

263 papers.

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  1. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  2. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  3. 2021Score-based Generative Modeling in Latent Spacecited by 634
  4. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  5. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 577
  6. 2022DiGress: Discrete Denoising diffusion for graph generationcited by 503
  7. 2021Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speechcited by 445
  8. 2023ResShift: Efficient Diffusion Model for Image Super-resolution by Residual Shiftingcited by 360
  9. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecastingcited by 332
  10. 2021Score-based diffusion models for accelerated MRIcited by 308
  11. 2022Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equationscited by 273
  12. 2023Q-Diffusion: Quantizing Diffusion Modelscited by 266
38 more
  1. 2022Post-training Quantization on Diffusion Modelscited by 262
  2. 2022A Survey on Generative Diffusion Modelcited by 238
  3. 2021Gotta Go Fast When Generating Data with Score-Based Modelscited by 218
  4. 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimizationcited by 216
  5. 2022Concrete Score Matching: Generalized Score Matching for Discrete Datacited by 144
  6. 2022Diffusion Models for Video Prediction and Infillingcited by 134
  7. 2022GENIE: Higher-Order Denoising Diffusion Solverscited by 127
  8. 2022Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimizationcited by 118
  9. 2024InstructScene: Instruction-Driven 3D Indoor Scene Synthesis with Semantic Graph Priorcited by 110
  10. 2021D2C: Diffusion-Denoising Models for Few-shot Conditional Generationcited by 96
  11. 2022SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generatorscited by 96
  12. 2022DifFace: Blind Face Restoration with Diffused Error Contractioncited by 96
  13. 2022Exploring Chemical Space with Score-based Out-of-distribution Generationcited by 95
  14. 2024Physics-Informed Diffusion Modelscited by 88
  15. 2021GraphEBM: Molecular Graph Generation with Energy-Based Modelscited by 85
  16. 2023A Complete Survey on Generative AI (AIGC): Is ChatGPT from GPT-4 to GPT-5 All You Need?cited by 84
  17. 2023Autoregressive Diffusion Model for Graph Generationcited by 82
  18. 2023DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Modelscited by 81
  19. 2023Diffusion-Based 3D Human Pose Estimation with Multi-Hypothesis Aggregationcited by 81
  20. 2023Generative Diffusion Models on Graphs: Methods and Applicationscited by 79
  21. 2024Variational Flow Matching for Graph Generationcited by 78
  22. 2023Efficient and Degree-Guided Graph Generation via Discrete Diffusion Modelingcited by 75
  23. 2024Discrete-state Continuous-time Diffusion for Graph Generationcited by 73
  24. 2022A Survey on Deep Graph Generation: Methods and Applicationscited by 69
  25. 2022Diffusion Models for Graphs Benefit From Discrete State Spacescited by 69
  26. 2023MolDiff: Addressing the Atom-Bond Inconsistency Problem in 3D Molecule Diffusion Generationcited by 65
  27. 2022Measurement-conditioned Denoising Diffusion Probabilistic Model for Under-sampled Medical Image Reconstructioncited by 64
  28. 2022Progressive Distillation for Fast Sampling of Diffusion Modelscited by 61
  29. 2023Generating and Imputing Tabular Data via Diffusion and Flow-based Gradient-Boosted Treescited by 60
  30. 2021Diffusion-Based Representation Learningcited by 57
  31. 2023Enhancing Deep Reinforcement Learning: A Tutorial on Generative Diffusion Models in Network Optimizationcited by 56
  32. 2023Graph Generation with Diffusion Mixturecited by 52
  33. 2023Scalable Diffusion for Materials Generationcited by 52
  34. 2024How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Frameworkcited by 48
  35. 2025Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithmscited by 47
  36. 2023Conditional Diffusion Based on Discrete Graph Structures for Molecular Graph Generationcited by 46
  37. 2024Graph Diffusion Transformers for Multi-Conditional Molecular Generationcited by 44
  38. 2024Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformizationcited by 44

50 most cited of 263 All 263 (JSON)

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