Generator-based Graph Generation via Heat Diffusion

2026-02-03

AI Summary

This work addresses the challenge of graph generation by proposing a continuous-time diffusion framework grounded in the graph Laplacian. The approach defines conditional perturbations via the heat kernel, approximates its infinitesimal generator using neural networks, and synthesizes new graphs through reverse diffusion sampling. By integrating the generator matching principle into graph generation, the method effectively combines spectral graph priors with the expressive power of neural networks, thereby unifying and generalizing existing diffusion-based models. Experimental results demonstrate that the proposed framework accurately captures essential topological characteristics across both real-world and synthetic graphs, achieving superior generation quality and strong generalization capabilities.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Natural Language Processing: Generation
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

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.

Problem

• graph generation
• heat diffusion
• graph Laplacian
• generative modeling
• structural properties

Innovation

• Generator Matching
• Heat Diffusion
• Graph Laplacian
• Bregman Divergence
• Continuous-time Diffusion