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、图像到文本转换及视频生成等多种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，具有诸多实际应用场景，其核心目标在于学习给定图的分布规律并生成新图。鉴于扩散模型在图像生成领域的卓越表现，近年来学术界日益重视利用这些技术推动图生成的发展。本文首先系统综述了图上的生成扩散模型，重点梳理了图扩散模型三类变体的代表性算法，即基于朗之万动力学的分数匹配（SMLD）、去噪扩散概率模型（DDPM）与基于分数的生成模型（SGM）。继而，我们总结了生成扩散模型在图数据上的主要应用，特别聚焦于分子与蛋白质建模领域。最后，我们探讨了基于图结构数据的生成扩散模型未来具有前景的研究方向。