  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. For this survey, we also created a
GitHub project website by collecting the supporting resources for generative
diffusion models on graphs, at the link:
https://github.com/ChengyiLIU-cs/Generative-Diffusion-Models-on-Graphs
