用热扩散机制生成图结构，兼顾领域先验与神经网络灵活性。
Generator-based Graph Generation via Heat Diffusion
- 基于图拉普拉斯和热核定义连续时间扩散过程
- 训练神经网络匹配生成器，实现图结构采样
- 适合需要结构可控的图生成任务
图生成建模因在化学、生物、社交网络和知识表示等领域的广泛应用而变得至关重要。本文提出一种新框架，将生成匹配（Generator Matching）范式应用于图结构数据。利用图拉普拉斯及其关联的热核，在每个图上定义连续时间扩散过程。拉普拉斯作为该扩散的无穷小生成子，其热核提供初始图的一族条件扰动。通过最小化真实生成子与可学习代理生成子之间的Bregman散度，训练神经网络以匹配该生成子。训练完成后，使用代理生成子模拟时间反向扩散过程，生成新的图结构。该框架统一并推广了现有的基于扩散的图生成模型，通过拉普拉斯注入领域特定归纳偏置，同时保留神经近似器的灵活性。实验表明，该方法能有效捕捉真实与合成图的结构特性。
原文摘要 · Abstract (English)
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.
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