mlsanityData to 7 Oct 2026

SwinGNN: Rethinking Permutation Invariance in Diffusion Models for Graph Generation

arXiv 2307.01646 ↗First posted 4 Jul 2023cs.LG cs.AIcited by 26

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

Abstract (arXiv)

Diffusion models based on permutation-equivariant networks can learn permutation-invariant distributions for graph data. However, in comparison to their non-invariant counterparts, we have found that these invariant models encounter greater learning challenges since 1) their effective target distributions exhibit more modes; 2) their optimal one-step denoising scores are the score functions of Gaussian mixtures with more components. Motivated by this analysis, we propose a non-invariant diffusion model, called textitSwinGNN, which employs an efficient edge-to-edge 2-WL message passing network and utilizes shifted window based self-attention inspired by SwinTransformers. Further, through systematic ablations, we identify several critical training and sampling techniques that significantly improve the sample quality of graph generation. At last, we introduce a simple post-processing trick, textiti.e., randomly permuting the generated graphs, which provably converts any graph generative model to a permutation-invariant one. Extensive experiments on synthetic and real-world protein and molecule datasets show that our SwinGNN achieves state-of-the-art performances. Our code is released at https://github.com/qiyan98/SwinGNN.

Key facts. Cited by 26 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 54 of its 80 references that are in the map. First posted on arXiv 4 Jul 2023.

Builds on

54 of 80 references.

Closest ancestors · 5

Same direction, newest first

  1. 2022DiGress: Discrete Denoising diffusion for graph generation29 Sep
  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 · 49

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2021Swin Transformer: Hierarchical Vision Transformer using Shifted Windowscited by 12,082
  4. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  5. 2020Denoising Diffusion Implicit Modelscited by 9,655
  6. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  7. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  8. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  9. 2018How Powerful are Graph Neural Networks?cited by 4,355
  10. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  11. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  12. 2022Imagen Video: High Definition Video Generation with Diffusion Modelscited by 1,765
37 more
  1. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  2. 2016Variational Graph Auto-Encoderscited by 1,373
  3. 2018Unified Perceptual Parsing for Scene Understandingcited by 1,265
  4. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  5. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  6. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 878
  7. 2018Junction Tree Variational Autoencoder for Molecular Graph Generationcited by 647
  8. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 566
  9. 2018GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Modelscited by 406
  10. 2018MolGAN: An implicit generative model for small molecular graphscited by 392
  11. 2019Provably Powerful Graph Networkscited by 385
  12. 2018GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoderscited by 375
  13. 2022Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioningcited by 362
  14. 2018Invariant and Equivariant Graph Networkscited by 339
  15. 2020GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generationcited by 301
  16. 2019Efficient Graph Generation with Graph Recurrent Attention Networkscited by 231
  17. 2018Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discoverycited by 191
  18. 2021GraphDF: A Discrete Flow Model for Molecular Graph Generationcited by 177
  19. 2019On the equivalence between graph isomorphism testing and function approximation with GNNscited by 172
  20. 2021Weisfeiler and Leman go Machine Learning: The Story so farcited by 121
  21. 2019GraphNVP: An Invertible Flow Model for Generating Molecular Graphscited by 115
  22. 2021Energy-Based Learning for Scene Graph Generationcited by 104
  23. 2019Graph Normalizing Flowscited by 103
  24. 2022SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generatorscited by 96
  25. 2023Diffusion-Based 3D Human Pose Estimation with Multi-Hypothesis Aggregationcited by 81
  26. 2018Generative Code Modeling with Graphscited by 59
  27. 2020Categorical Normalizing Flows via Continuous Transformationscited by 36
  28. 2021Top-N: Equivariant set and graph generation without exchangeabilitycited by 36
  29. 2019Neural Turtle Graphics for Modeling City Road Layoutscited by 29
  30. 2022Towards Better Out-of-Distribution Generalization of Neural Algorithmic Reasoning Taskscited by 29
  31. 2014Near-optimal-sample estimators for spherical Gaussian mixturescited by 26
  32. 2021Beyond In-Place Corruption: Insertion and Deletion In Denoising Probabilistic Modelscited by 23
  33. 2018Practical bounds on the error of Bayesian posterior approximations: A nonasymptotic approachcited by 12
  34. 2023What functions can Graph Neural Networks compute on random graphs? The role of Positional Encodingcited by 11
  35. 2022Micro and Macro Level Graph Modeling for Graph Variational Auto-Encoderscited by 8
  36. 2022What Functions Can Graph Neural Networks Generate?cited by 5
  37. 2022GraphPNAS: Learning Distribution of Good Neural Architectures via Deep Graph Generative Modelscited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 9; 2025: 8; 2026: 6.

26 papers.

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  1. 2024Utilizing Image Transforms and Diffusion Models for Generative Modeling of Short and Long Time Seriescited by 42
  2. 2023Efficient and Scalable Graph Generation through Iterative Local Expansioncited by 35
  3. 2025MoFlow: One-Step Flow Matching for Human Trajectory Forecasting via Implicit Maximum Likelihood Estimation based Distillationcited by 31
  4. 2024Pard: Permutation-Invariant Autoregressive Diffusion for Graph Generationcited by 25
  5. 2024Generative Modelling of Structurally Constrained Graphscited by 17
  6. 2023A Simple and Scalable Representation for Graph Generationcited by 15
  7. 2024Improving Molecular Graph Generation with Flow Matching and Optimal Transportcited by 10
  8. 2024Equivariant Denoisers Cannot Copy Graphs: Align Your Graph Diffusion Modelscited by 7
  9. 2025TrajFlow: Multi-modal Motion Prediction via Flow Matchingcited by 7
  10. 2024Reviving Life on the Edge: Joint Score-Based Graph Generation of Rich Edge Attributescited by 6
  11. 2024Generating Physical Dynamics under Priorscited by 6
  12. 2025FragFM: Hierarchical Framework for Efficient Molecule Generation via Fragment-Level Discrete Flow Matchingcited by 5
14 more
  1. 2026Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generationcited by 5
  2. 2024Joint Generative Modeling of Grounded Scene Graphs and Images via Diffusion Modelscited by 4
  3. 2025DDPS: Discrete Diffusion Posterior Sampling for Paths in Layered Graphscited by 4
  4. 2025RETRO SYNFLOW: Discrete Flow Matching for Accurate and Diverse Single-Step Retrosynthesiscited by 4
  5. 2025Diffusion-Free Graph Generation with Next-Scale Predictioncited by 3
  6. 2023Generative AI-Based Probabilistic Constellation Shaping With Diffusion Modelscited by 2
  7. 2026ACDZero: MCTS Agent for Mastering Automated Cyber Defensecited by 2
  8. 2024SeaDAG: Semi-autoregressive Diffusion for Conditional Directed Acyclic Graph Generationcited by 1
  9. 2025Graph VQ-Transformer (GVT): Fast and Accurate Molecular Generation via High-Fidelity Discrete Latentscited by 1
  10. 2025Subgraph Generation for Generalizing on Out-of-Distribution Linkscited by 0
  11. 2026Balancing Symmetry and Efficiency in Graph Flow Matchingcited by 0
  12. 2026Modular Diffusion Models for Structured Visual Recognitioncited by 0
  13. 2026From topology learning to graph generation: A unifying perspectivecited by 0
  14. 2026GLASS: Global Latent Aggregation with Slot-based Set Decoding for Scalable All-Atom Crystal Generationcited by 0

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