# Generator-based Graph Generation via Heat Diffusion

arXiv: https://arxiv.org/abs/2602.03612 · HTML: https://mlsanity.com/paper/2602.03612/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 32 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 21 of 21)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [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)
- [GuacaMol: Benchmarking Models for De Novo Molecular Design](https://mlsanity.com/paper/1811.09621/) (2018)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [GraphGAN: Graph Representation Learning with Generative Adversarial Nets](https://mlsanity.com/paper/1711.08267/) (2017)
- [SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators](https://mlsanity.com/paper/2204.01613/) (2022)
- [Generator Matching: Generative modeling with arbitrary Markov processes](https://mlsanity.com/paper/2410.20587/) (2024)
- [DeFoG: Discrete Flow Matching for Graph Generation](https://mlsanity.com/paper/2410.04263/) (2024)
- [On Evaluation Metrics for Graph Generative Models](https://mlsanity.com/paper/2201.09871/) (2022)
- [Metrics for Graph Comparison: A Practitioner's Guide](https://mlsanity.com/paper/1904.07414/) (2019)
- [Covariate-assisted spectral clustering](https://mlsanity.com/paper/1411.2158/) (2014)
- [GNNEvaluator: Evaluating GNN Performance On Unseen Graphs Without Labels](https://mlsanity.com/paper/2310.14586/) (2023)
- [Privacy-Preserving Graph Machine Learning from Data to Computation: A Survey](https://mlsanity.com/paper/2307.04338/) (2023)

## Built on by (most cited first, 1 of 1)

- [Hypergraph Generation via Structured Stochastic Diffusion](https://mlsanity.com/paper/2605.05024/) (2026)

## Abstract (arXiv)

Graph generative modelling has become an essential task due to the wide range of applications in chemistry, biology, social networks, and knowledge representation. In this work, we propose a novel framework for generating graphs by adapting the Generator Matching (arXiv:2410.20587) paradigm to graph-structured data. We leverage the graph Laplacian and its associated heat kernel to define a continous-time diffusion on each graph. The Laplacian serves as the infinitesimal generator of this diffusion, and its heat kernel provides a family of conditional perturbations of the initial graph. A neural network is trained to match this generator by minimising a Bregman divergence between the true generator and a learnable surrogate. Once trained, the surrogate generator is used to simulate a time-reversed diffusion process to sample new graph structures. Our framework unifies and generalises existing diffusion-based graph generative models, injecting domain-specific inductive bias via the Laplacian, while retaining the flexibility of neural approximators. Experimental studies demonstrate that our approach captures structural properties of real and synthetic graphs effectively.