mlsanityData to 7 Oct 2026

Fast Graph Generation via Spectral Diffusion

arXiv 2211.08892 ↗First posted 16 Nov 2022cs.LG cs.AIcited by 36

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

Abstract (arXiv)

Generating graph-structured data is a challenging problem, which requires learning the underlying distribution of graphs. Various models such as graph VAE, graph GANs, and graph diffusion models have been proposed to generate meaningful and reliable graphs, among which the diffusion models have achieved state-of-the-art performance. In this paper, we argue that running full-rank diffusion SDEs on the whole graph adjacency matrix space hinders diffusion models from learning graph topology generation, and hence significantly deteriorates the quality of generated graph data. To address this limitation, we propose an efficient yet effective Graph Spectral Diffusion Model (GSDM), which is driven by low-rank diffusion SDEs on the graph spectrum space. Our spectral diffusion model is further proven to enjoy a substantially stronger theoretical guarantee than standard diffusion models. Extensive experiments across various datasets demonstrate that, our proposed GSDM turns out to be the SOTA model, by exhibiting both significantly higher generation quality and much less computational consumption than the baselines.

Key facts. Cited by 36 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 29 of its 39 references that are in the map. First posted on arXiv 16 Nov 2022.

Builds on

29 of 39 references.

Closest ancestors · 3

Same direction, newest first

  1. 2022Protein structure generation via folding diffusion30 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 · 26

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  2. 2022Classifier-Free Diffusion Guidancecited by 5,717
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  4. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  5. 2021Variational Diffusion Modelscited by 1,145
  6. 2019Improved Precision and Recall Metric for Assessing Generative Modelscited by 925
  7. 2020TUDataset: A collection of benchmark datasets for learning with graphscited by 718
  8. 2018GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Modelscited by 406
  9. 2018MolGAN: An implicit generative model for small molecular graphscited by 392
  10. 2018GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoderscited by 375
  11. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
  12. 2020GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generationcited by 301
14 more
  1. 2018Learning Deep Generative Models of Graphscited by 227
  2. 2018Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discoverycited by 191
  3. 2020MoFlow: An Invertible Flow Model for Generating Molecular Graphscited by 183
  4. 2021GraphDF: A Discrete Flow Model for Molecular Graph Generationcited by 177
  5. 2019Graph Normalizing Flowscited by 103
  6. 2020A Systematic Survey on Deep Generative Models for Graph Generationcited by 94
  7. 2021GraphEBM: Molecular Graph Generation with Energy-Based Modelscited by 85
  8. 2020Factorizable Graph Convolutional Networkscited by 79
  9. 2018Constrained Generation of Semantically Valid Graphs via Regularizing Variational Autoencoderscited by 74
  10. 2022Subspace Diffusion Generative Modelscited by 70
  11. 2022Wavelet Score-Based Generative Modelingcited by 61
  12. 2021Rapid Neural Architecture Search by Learning to Generate Graphs from Datasetscited by 33
  13. 2019MCNE: An End-to-End Framework for Learning Multiple Conditional Network Representations of Social Networkcited by 31
  14. 2017Global Optimization with Orthogonality Constraints via Stochastic Diffusion on Manifoldcited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 5; 2024: 11; 2025: 15; 2026: 5.

36 papers.

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  1. 2023On the Design Fundamentals of Diffusion Models: A Surveycited by 59
  2. 2024Data Augmentation using Large Language Models: Data Perspectives, Learning Paradigms and Challengescited by 30
  3. 2024Cometh: A continuous-time discrete-state graph diffusion modelcited by 29
  4. 2024Diffusion Models in textitDe Novo Drug Designcited by 26
  5. 2023Data-centric Graph Learning: A Surveycited by 22
  6. 2024Geometric Representation Condition Improves Equivariant Molecule Generationcited by 13
  7. 2024LDMol: A Text-to-Molecule Diffusion Model with Structurally Informative Latent Space Surpasses AR Modelscited by 11
  8. 2023MASA-TCN: Multi-anchor Space-aware Temporal Convolutional Neural Networks for Continuous and Discrete EEG Emotion Recognitioncited by 9
  9. 2024Two Trades is not Baffled: Condensing Graph via Crafting Rational Gradient Matchingcited by 8
  10. 2024Generating Graphs via Spectral Diffusioncited by 8
  11. 2025HOG-Diff: Higher-Order Guided Diffusion for Graph Generationcited by 6
  12. 2025Artificial Intelligence in Spectroscopy: Advancing Chemistry from Prediction to Generation and Beyondcited by 6
24 more
  1. 2025CycleDiff: Cycle Diffusion Models for Unpaired Image-to-image Translationcited by 6
  2. 2024SpecSTG: A Fast Spectral Diffusion Framework for Probabilistic Spatio-Temporal Traffic Forecastingcited by 5
  3. 2025FragFM: Hierarchical Framework for Efficient Molecule Generation via Fragment-Level Discrete Flow Matchingcited by 5
  4. 2025Graph Guided Diffusion: Unified Guidance for Conditional Graph Generationcited by 5
  5. 2025Controllable Graph Generation with Diffusion Models via Inference-Time Tree Search Guidancecited by 5
  6. 2026Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generationcited by 5
  7. 2023RGCVAE: Relational Graph Conditioned Variational Autoencoder for Molecule Designcited by 3
  8. 2024Stealing Training Graphs from Graph Neural Networkscited by 3
  9. 2023Modeling and design of heterogeneous hierarchical bioinspired spider web structures using generative deep learning and additive manufacturingcited by 2
  10. 2024Diffusion-based Graph Generative Methodscited by 2
  11. 2025Graph Generation with Spectral Geodesic Flow Matchingcited by 2
  12. 2025Toward a Unified Geometry Understanding: Riemannian Diffusion Framework for Graph Generation and Predictioncited by 1
  13. 2025Transport-Coupled Bayesian Flows for Molecular Graph Generationcited by 1
  14. 2026Variational Bayesian Flow Network for Graph Generationcited by 1
  15. 2026Bias mitigation in graph diffusion modelscited by 1
  16. 2024Combinatorial Complex Score-based Diffusion Modelling through Stochastic Differential Equationscited by 0
  17. 2025You Only Look One Step: Accelerating Backpropagation in Diffusion Sampling with Gradient Shortcutscited by 0
  18. 2025GSDNet: Revisiting Incomplete Multimodal-Diffusion from Graph Spectrum Perspective for Conversation Emotion Recognitioncited by 0
  19. 2025GraphWeave: Interpretable and Robust Graph Generation via Random Walk Trajectoriescited by 0
  20. 2025Permutation-Invariant Spectral Learning via Dyson Diffusioncited by 0
  21. 2025Generative Myopia: Why Diffusion Models Fail at Structurecited by 0
  22. 2025GFT-GCN: Privacy-Preserving 3D Face Mesh Recognition with Spectral Diffusioncited by 0
  23. 2026Mitigating topology biases in Graph Diffusion via Counterfactual Interventioncited by 0
  24. 2026Efficient Synthetic Network Generation via Latent Embedding Reconstructioncited by 0

Similar, not cited

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  1. 2023Autoregressive Diffusion Model for Graph Generation
  2. 2023Efficient and Degree-Guided Graph Generation via Discrete Diffusion Modeling
  3. 2025Do Graph Diffusion Models Accurately Capture and Generate Substructure Distributions?
  4. 2023Graph Generation with Diffusion Mixture
  5. 2026Discrete Diffusion for Large Graph Generation via Structural Candidate Restriction
  6. 2024Discrete-state Continuous-time Diffusion for Graph Generation
  7. 2025SBGD: Improving Graph Diffusion Generative Model via Stochastic Block Diffusion
  8. 2024Advancing Graph Generation through Beta Diffusion