# GraphGDP: Generative Diffusion Processes for Permutation Invariant Graph Generation

arXiv: https://arxiv.org/abs/2212.01842 · HTML: https://mlsanity.com/paper/2212.01842/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 59 references that are in the map.
- First posted on arXiv 4 Dec 2022.

## Builds on (most cited first, 30 of 42)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [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)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [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)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [Learning Deep Generative Models of Graphs](https://mlsanity.com/paper/1803.03324/) (2018)
- [Position-aware Graph Neural Networks](https://mlsanity.com/paper/1906.04817/) (2019)
- [Constrained Graph Variational Autoencoders for Molecule Design](https://mlsanity.com/paper/1805.09076/) (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)
- [NetGAN: Generating Graphs via Random Walks](https://mlsanity.com/paper/1803.00816/) (2018)
- [Weisfeiler and Leman go Machine Learning: The Story so far](https://mlsanity.com/paper/2112.09992/) (2021)

## Built on by (most cited first, 30 of 43)

- [MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generation](https://mlsanity.com/paper/2302.09048/) (2023)
- [A Complete Survey on Generative AI (AIGC): Is ChatGPT from GPT-4 to GPT-5 All You Need?](https://mlsanity.com/paper/2303.11717/) (2023)
- [Generative Diffusion Models on Graphs: Methods and Applications](https://mlsanity.com/paper/2302.02591/) (2023)
- [Discrete-state Continuous-time Diffusion for Graph Generation](https://mlsanity.com/paper/2405.11416/) (2024)
- [PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputation](https://mlsanity.com/paper/2302.09746/) (2023)
- [Improving 3D Imaging with Pre-Trained Perpendicular 2D Diffusion Models](https://mlsanity.com/paper/2303.08440/) (2023)
- [Conditional Diffusion Based on Discrete Graph Structures for Molecular Graph Generation](https://mlsanity.com/paper/2301.00427/) (2023)
- [DiffKG: Knowledge Graph Diffusion Model for Recommendation](https://mlsanity.com/paper/2312.16890/) (2023)
- [A Survey on Graph Diffusion Models: Generative AI in Science for Molecule, Protein and Material](https://mlsanity.com/paper/2304.01565/) (2023)
- [Learning Joint 2D & 3D Diffusion Models for Complete Molecule Generation](https://mlsanity.com/paper/2305.12347/) (2023)
- [Data-centric Graph Learning: A Survey](https://mlsanity.com/paper/2310.04987/) (2023)
- [ArtFormer: Controllable Generation of Diverse 3D Articulated Objects](https://mlsanity.com/paper/2412.07237/) (2024)
- [Hyperbolic Geometric Latent Diffusion Model for Graph Generation](https://mlsanity.com/paper/2405.03188/) (2024)
- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [3D Vessel Graph Generation Using Denoising Diffusion](https://mlsanity.com/paper/2407.05842/) (2024)
- [Generating Graphs via Spectral Diffusion](https://mlsanity.com/paper/2402.18974/) (2024)
- [Equivariant Denoisers Cannot Copy Graphs: Align Your Graph Diffusion Models](https://mlsanity.com/paper/2405.17656/) (2024)
- [GALA: Graph Diffusion-based Alignment with Jigsaw for Source-free Domain Adaptation](https://mlsanity.com/paper/2410.16606/) (2024)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [Diffusion Twigs with Loop Guidance for Conditional Graph Generation](https://mlsanity.com/paper/2410.24012/) (2024)
- [Size Matters: Large Graph Generation with HiGGs](https://mlsanity.com/paper/2306.11412/) (2023)
- [Sum-Product-Set Networks: Deep Tractable Models for Tree-Structured Graphs](https://mlsanity.com/paper/2408.07394/) (2024)
- [TDNetGen: Empowering Complex Network Resilience Prediction with Generative Augmentation of Topology and Dynamics](https://mlsanity.com/paper/2408.09825/) (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)
- [Graph Neural Stochastic Differential Equations](https://mlsanity.com/paper/2308.12316/) (2023)
- [Diffusion-based Graph Generative Methods](https://mlsanity.com/paper/2401.15617/) (2024)
- [Theoretical research on generative diffusion models: an overview](https://mlsanity.com/paper/2404.09016/) (2024)
- [Toward Real-World Table Agents: Capabilities, Workflows, and Design Principles for LLM-based Table Intelligence](https://mlsanity.com/paper/2507.10281/) (2025)
- [Inference Attacks Against Graph Generative Diffusion Models](https://mlsanity.com/paper/2601.03701/) (2026)
- [Probabilistic Graph Circuits: Deep Generative Models for Tractable Probabilistic Inference over Graphs](https://mlsanity.com/paper/2503.12162/) (2025)

## Abstract (arXiv)

Graph generative models have broad applications in biology, chemistry and social science. However, modelling and understanding the generative process of graphs is challenging due to the discrete and high-dimensional nature of graphs, as well as permutation invariance to node orderings in underlying graph distributions. Current leading autoregressive models fail to capture the permutation invariance nature of graphs for the reliance on generation ordering and have high time complexity. Here, we propose a continuous-time generative diffusion process for permutation invariant graph generation to mitigate these issues. Specifically, we first construct a forward diffusion process defined by a stochastic differential equation (SDE), which smoothly converts graphs within the complex distribution to random graphs that follow a known edge probability. Solving the corresponding reverse-time SDE, graphs can be generated from newly sampled random graphs. To facilitate the reverse-time SDE, we newly design a position-enhanced graph score network, capturing the evolving structure and position information from perturbed graphs for permutation equivariant score estimation. Under the evaluation of comprehensive metrics, our proposed generative diffusion process achieves competitive performance in graph distribution learning. Experimental results also show that GraphGDP can generate high-quality graphs in only 24 function evaluations, much faster than previous autoregressive models.