Abstract: Generative artificial intelligence represented by diffusion models has significantly contributed to medical imaging reconstruction. To help researchers comprehensively understand the rich content of diffusion models, this review provides a detailed overview of diffusion models used in medical imaging reconstruction. The theoretical foundation and fundamental concepts underlying the diffusion modeling framework were first introduced, describing their origin and evolution. Second, a systematic characteristic-based taxonomy of diffusion models used in medical imaging reconstruction is provided, broadly covering their application to imaging modalities, including MRI, CT, PET, and PAI. Finally, we discuss the limitations of current diffusion models and anticipate potential directions of future research, providing an intuitive starting point for subsequent exploratory research. Related codes are available at GitHub: https://github.com/yqx7150/Diffusion-Models-for-Medical-Imaging.