# Fast Graph Generation via Spectral Diffusion

arXiv: https://arxiv.org/abs/2211.08892 · HTML: https://mlsanity.com/paper/2211.08892/

## Key facts

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

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 29 of 29)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Learning Deep Generative Models of Graphs](https://mlsanity.com/paper/1803.03324/) (2018)
- [Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discovery](https://mlsanity.com/paper/1803.09518/) (2018)
- [MoFlow: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/2006.10137/) (2020)
- [GraphDF: A Discrete Flow Model for Molecular Graph Generation](https://mlsanity.com/paper/2102.01189/) (2021)
- [Protein structure generation via folding diffusion](https://mlsanity.com/paper/2209.15611/) (2022)
- [Graph Normalizing Flows](https://mlsanity.com/paper/1905.13177/) (2019)
- [A Systematic Survey on Deep Generative Models for Graph Generation](https://mlsanity.com/paper/2007.06686/) (2020)
- [GraphEBM: Molecular Graph Generation with Energy-Based Models](https://mlsanity.com/paper/2102.00546/) (2021)
- [Factorizable Graph Convolutional Networks](https://mlsanity.com/paper/2010.05421/) (2020)
- [Constrained Generation of Semantically Valid Graphs via Regularizing Variational Autoencoders](https://mlsanity.com/paper/1809.02630/) (2018)
- [Subspace Diffusion Generative Models](https://mlsanity.com/paper/2205.01490/) (2022)
- [Wavelet Score-Based Generative Modeling](https://mlsanity.com/paper/2208.05003/) (2022)
- [Rapid Neural Architecture Search by Learning to Generate Graphs from Datasets](https://mlsanity.com/paper/2107.00860/) (2021)
- [MCNE: An End-to-End Framework for Learning Multiple Conditional Network Representations of Social Network](https://mlsanity.com/paper/1905.11013/) (2019)
- [Global Optimization with Orthogonality Constraints via Stochastic Diffusion on Manifold](https://mlsanity.com/paper/1707.02126/) (2017)

## Built on by (most cited first, 30 of 36)

- [On the Design Fundamentals of Diffusion Models: A Survey](https://mlsanity.com/paper/2306.04542/) (2023)
- [Cometh: A continuous-time discrete-state graph diffusion model](https://mlsanity.com/paper/2406.06449/) (2024)
- [Data Augmentation using Large Language Models: Data Perspectives, Learning Paradigms and Challenges](https://mlsanity.com/paper/2403.02990/) (2024)
- [Diffusion Models in textitDe Novo Drug Design](https://mlsanity.com/paper/2406.08511/) (2024)
- [Data-centric Graph Learning: A Survey](https://mlsanity.com/paper/2310.04987/) (2023)
- [Geometric Representation Condition Improves Equivariant Molecule Generation](https://mlsanity.com/paper/2410.03655/) (2024)
- [LDMol: A Text-to-Molecule Diffusion Model with Structurally Informative Latent Space Surpasses AR Models](https://mlsanity.com/paper/2405.17829/) (2024)
- [MASA-TCN: Multi-anchor Space-aware Temporal Convolutional Neural Networks for Continuous and Discrete EEG Emotion Recognition](https://mlsanity.com/paper/2308.16207/) (2023)
- [Two Trades is not Baffled: Condensing Graph via Crafting Rational Gradient Matching](https://mlsanity.com/paper/2402.04924/) (2024)
- [Generating Graphs via Spectral Diffusion](https://mlsanity.com/paper/2402.18974/) (2024)
- [HOG-Diff: Higher-Order Guided Diffusion for Graph Generation](https://mlsanity.com/paper/2502.04308/) (2025)
- [FragFM: Hierarchical Framework for Efficient Molecule Generation via Fragment-Level Discrete Flow Matching](https://mlsanity.com/paper/2502.15805/) (2025)
- [CycleDiff: Cycle Diffusion Models for Unpaired Image-to-image Translation](https://mlsanity.com/paper/2508.06625/) (2025)
- [Controllable Graph Generation with Diffusion Models via Inference-Time Tree Search Guidance](https://mlsanity.com/paper/2510.10402/) (2025)
- [Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation](https://mlsanity.com/paper/2602.15022/) (2026)
- [Artificial Intelligence in Spectroscopy: Advancing Chemistry from Prediction to Generation and Beyond](https://mlsanity.com/paper/2502.09897/) (2025)
- [SpecSTG: A Fast Spectral Diffusion Framework for Probabilistic Spatio-Temporal Traffic Forecasting](https://mlsanity.com/paper/2401.08119/) (2024)
- [Graph Guided Diffusion: Unified Guidance for Conditional Graph Generation](https://mlsanity.com/paper/2505.19685/) (2025)
- [RGCVAE: Relational Graph Conditioned Variational Autoencoder for Molecule Design](https://mlsanity.com/paper/2305.11699/) (2023)
- [Stealing Training Graphs from Graph Neural Networks](https://mlsanity.com/paper/2411.11197/) (2024)
- [Modeling and design of heterogeneous hierarchical bioinspired spider web structures using generative deep learning and additive manufacturing](https://mlsanity.com/paper/2304.05137/) (2023)
- [Diffusion-based Graph Generative Methods](https://mlsanity.com/paper/2401.15617/) (2024)
- [Graph Generation with Spectral Geodesic Flow Matching](https://mlsanity.com/paper/2510.02520/) (2025)
- [Toward a Unified Geometry Understanding: Riemannian Diffusion Framework for Graph Generation and Prediction](https://mlsanity.com/paper/2510.04522/) (2025)
- [Transport-Coupled Bayesian Flows for Molecular Graph Generation](https://mlsanity.com/paper/2510.10211/) (2025)
- [Variational Bayesian Flow Network for Graph Generation](https://mlsanity.com/paper/2601.22524/) (2026)
- [Bias mitigation in graph diffusion models](https://mlsanity.com/paper/2604.01709/) (2026)
- [Combinatorial Complex Score-based Diffusion Modelling through Stochastic Differential Equations](https://mlsanity.com/paper/2406.04916/) (2024)
- [You Only Look One Step: Accelerating Backpropagation in Diffusion Sampling with Gradient Shortcuts](https://mlsanity.com/paper/2505.07477/) (2025)
- [GSDNet: Revisiting Incomplete Multimodal-Diffusion from Graph Spectrum Perspective for Conversation Emotion Recognition](https://mlsanity.com/paper/2506.12325/) (2025)

## 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.