Diffusion models have rapidly emerged as a new paradigm in generative modeling. Therefore, we aim to provide a comprehensive review of graph diffusion models. We introduce various forms of diffusion models (i.e., DDPMs, SDEs, and SGMs), their working mechanisms, and how they can be extended to graph data. Specifically, graph diffusion models follow the modeling process of diffusion models, implement the diffusion process in graph data, and gradually denoise and generate new graph structures through reverse steps. The application of graph diffusion models is mainly focused on the application scenarios of generating molecules and proteins, but graph diffusion models also show potential in recommendation systems and other fields. We explore the performance and advantages of graph diffusion models in these specific applications, such as using them to discover new drugs and predict protein structures. Furthermore, we also discuss the problem of evaluating graph diffusion models and their existing challenges. Due to the complexity and diversity of graph data, the authenticity of generated samples is an important and challenging task. We analyze their limitations and propose potential improvement directions to better measure the effectiveness of graph diffusion models. The summary of existing methods mentioned is in our Github: https://github.com/yuntaoshou/Graph-Diffusion-Models.
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