# Generative Diffusion Models on Graphs: Methods and Applications

arXiv: https://arxiv.org/abs/2302.02591 · HTML: https://mlsanity.com/paper/2302.02591/

## Key facts

- Cited by 81 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 77 of its 122 references that are in the map.
- First posted on arXiv 6 Feb 2023.

## 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, 30 of 77)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Explainability in Graph Neural Networks: A Taxonomic Survey](https://mlsanity.com/paper/2012.15445/) (2020)
- [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)
- [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)

## Built on by (most cited first, 30 of 81)

- [Recommender Systems in the Era of Large Language Models (LLMs)](https://mlsanity.com/paper/2307.02046/) (2023)
- [The Diffusion Duality](https://mlsanity.com/paper/2506.10892/) (2025)
- [Empowering Molecule Discovery for Molecule-Caption Translation with Large Language Models: A ChatGPT Perspective](https://mlsanity.com/paper/2306.06615/) (2023)
- [Discrete-state Continuous-time Diffusion for Graph Generation](https://mlsanity.com/paper/2405.11416/) (2024)
- [On the Design Fundamentals of Diffusion Models: A Survey](https://mlsanity.com/paper/2306.04542/) (2023)
- [Enhancing Deep Reinforcement Learning: A Tutorial on Generative Diffusion Models in Network Optimization](https://mlsanity.com/paper/2308.05384/) (2023)
- [Pyramid Diffusion for Fine 3D Large Scene Generation](https://mlsanity.com/paper/2311.12085/) (2023)
- [A Comprehensive Survey on Data Augmentation](https://mlsanity.com/paper/2405.09591/) (2024)
- [Fast Graph Condensation with Structure-based Neural Tangent Kernel](https://mlsanity.com/paper/2310.11046/) (2023)
- [Esoteric Language Models: A Family of Any-Order Diffusion LLMs](https://mlsanity.com/paper/2506.01928/) (2025)
- [Diffusion Models in textitDe Novo Drug Design](https://mlsanity.com/paper/2406.08511/) (2024)
- [NAP: Neural 3D Articulation Prior](https://mlsanity.com/paper/2305.16315/) (2023)
- [A Survey of Diffusion Based Image Generation Models: Issues and Their Solutions](https://mlsanity.com/paper/2308.13142/) (2023)
- [Pard: Permutation-Invariant Autoregressive Diffusion for Graph Generation](https://mlsanity.com/paper/2402.03687/) (2024)
- [Score-based Generative Diffusion Models for Social Recommendations](https://mlsanity.com/paper/2412.15579/) (2024)
- [A Deep Instance Generative Framework for MILP Solvers Under Limited Data Availability](https://mlsanity.com/paper/2310.02807/) (2023)
- [Absorb and Converge: Provable Convergence Guarantee for Absorbing Discrete Diffusion Models](https://mlsanity.com/paper/2506.02318/) (2025)
- [Discrete Diffusion Models: Novel Analysis and New Sampler Guarantees](https://mlsanity.com/paper/2509.16756/) (2025)
- [EditRoom: LLM-parameterized Graph Diffusion for Composable 3D Room Layout Editing](https://mlsanity.com/paper/2410.12836/) (2024)
- [The Diffusion Duality, Chapter II: Psi-Samplers](https://mlsanity.com/paper/2602.21185/) (2026)
- [Bures-Wasserstein Flow Matching for Graph Generation](https://mlsanity.com/paper/2506.14020/) (2025)
- [Sharp Convergence Rates for Masked Diffusion Models](https://mlsanity.com/paper/2602.22505/) (2026)
- [Diffusion and Flow Matching Models for Tabular Data: A Survey](https://mlsanity.com/paper/2502.17119/) (2025)
- [Graph-Aware Diffusion for Signal Generation](https://mlsanity.com/paper/2510.05036/) (2025)
- [Machine Learning Insides OptVerse AI Solver: Design Principles and Applications](https://mlsanity.com/paper/2401.05960/) (2024)
- [Reviving Life on the Edge: Joint Score-Based Graph Generation of Rich Edge Attributes](https://mlsanity.com/paper/2402.04046/) (2024)
- [Computational Protein Science in the Era of Large Language Models (LLMs)](https://mlsanity.com/paper/2501.10282/) (2025)
- [SpecSTG: A Fast Spectral Diffusion Framework for Probabilistic Spatio-Temporal Traffic Forecasting](https://mlsanity.com/paper/2401.08119/) (2024)
- [GDDA: Semantic OOD Detection on Graphs under Covariate Shift via Score-Based Diffusion Models](https://mlsanity.com/paper/2410.17526/) (2024)
- [GLProtein: Global-and-Local Structure Aware Protein Representation Learning](https://mlsanity.com/paper/2506.06294/) (2025)

## Abstract (arXiv)

Diffusion models, as a novel generative paradigm, have achieved remarkable success in various image generation tasks such as image inpainting, image-to-text translation, and video generation. Graph generation is a crucial computational task on graphs with numerous real-world applications. It aims to learn the distribution of given graphs and then generate new graphs. Given the great success of diffusion models in image generation, increasing efforts have been made to leverage these techniques to advance graph generation in recent years. In this paper, we first provide a comprehensive overview of generative diffusion models on graphs, In particular, we review representative algorithms for three variants of graph diffusion models, i.e., Score Matching with Langevin Dynamics (SMLD), Denoising Diffusion Probabilistic Model (DDPM), and Score-based Generative Model (SGM). Then, we summarize the major applications of generative diffusion models on graphs with a specific focus on molecule and protein modeling. Finally, we discuss promising directions in generative diffusion models on graph-structured data. For this survey, we also created a GitHub project website by collecting the supporting resources for generative diffusion models on graphs, at the link: https://github.com/ChengyiLIU-cs/Generative-Diffusion-Models-on-Graphs