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.

翻译：扩散模型作为一种新兴的生成范式，已在图像修复、图像转文本翻译及视频生成等各类图像生成任务中取得显著成功。图生成作为图计算领域的关键任务，具有众多现实应用场景，其核心目标是学习给定图的分布特征并生成新图。鉴于扩散模型在图像生成领域的巨大成就，近年来学界日益致力于将其技术迁移至图生成领域。本文首先对图上的生成扩散模型进行系统性综述，重点梳理三类图扩散模型变体的代表性算法：即朗之万动力学的分数匹配（SMLD）、去噪扩散概率模型（DDPM）及基于分数的生成模型（SGM）。继而总结生成扩散模型在图结构数据中的主要应用，特别聚焦于分子与蛋白质建模领域。最后，探讨图结构数据上生成扩散模型的未来研究方向。