Diffusion probabilistic models (DPMs) which employ explicit likelihood characterization and a gradual sampling process to synthesize data, have gained increasing research interest. Despite their huge computational burdens due to the large number of steps involved during sampling, DPMs are widely appreciated in various medical imaging tasks for their high-quality and diversity of generation. Magnetic resonance imaging (MRI) is an important medical imaging modality with excellent soft tissue contrast and superb spatial resolution, which possesses unique opportunities for DPMs. Although there is a recent surge of studies exploring DPMs in MRI, a survey paper of DPMs specifically designed for MRI applications is still lacking. This review article aims to help researchers in the MRI community to grasp the advances of DPMs in different applications. We first introduce the theory of two dominant kinds of DPMs, categorized according to whether the diffusion time step is discrete or continuous, and then provide a comprehensive review of emerging DPMs in MRI, including reconstruction, image generation, image translation, segmentation, anomaly detection, and further research topics. Finally, we discuss the general limitations as well as limitations specific to the MRI tasks of DPMs and point out potential areas that are worth further exploration.

翻译：扩散概率模型（DPMs）通过显式似然表征和渐进采样过程合成数据，近年来越来越受到研究关注。尽管由于采样过程中涉及大量步骤而导致计算负担巨大，但DPMs因其高质量和生成多样性而在各种医学成像任务中广受好评。核磁共振成像（MRI）是一种重要的医学成像模态，具有出色的软组织对比度和优异的空间分辨率，为DPMs提供了独特机遇。尽管近期涌现了大量探索DPM在MRI应用的研究，但专门针对MRI应用而设计的DPM综述论文仍然缺乏。本文旨在帮助MRI领域的研究人员掌握DPMs在不同应用中的进展。我们首先介绍了两种主要DPMs的理论（根据扩散时间步长是离散还是连续进行分类），然后全面综述了DPMs在MRI中的新兴应用，包括重建、图像生成、图像翻译、分割、异常检测及进一步的研究课题。最后，我们讨论了DPMs的一般局限性以及特定于MRI任务的局限性，并指出了值得进一步探索的潜在领域。