Denoising diffusion models, a class of generative models, have garnered immense interest lately in various deep-learning problems. A diffusion probabilistic model defines a forward diffusion stage where the input data is gradually perturbed over several steps by adding Gaussian noise and then learns to reverse the diffusion process to retrieve the desired noise-free data from noisy data samples. Diffusion models are widely appreciated for their strong mode coverage and quality of the generated samples despite their known computational burdens. Capitalizing on the advances in computer vision, the field of medical imaging has also observed a growing interest in diffusion models. To help the researcher navigate this profusion, this survey intends to provide a comprehensive overview of diffusion models in the discipline of medical image analysis. Specifically, we introduce the solid theoretical foundation and fundamental concepts behind diffusion models and the three generic diffusion modelling frameworks: diffusion probabilistic models, noise-conditioned score networks, and stochastic differential equations. Then, we provide a systematic taxonomy of diffusion models in the medical domain and propose a multi-perspective categorization based on their application, imaging modality, organ of interest, and algorithms. To this end, we cover extensive applications of diffusion models in the medical domain. Furthermore, we emphasize the practical use case of some selected approaches, and then we discuss the limitations of the diffusion models in the medical domain and propose several directions to fulfill the demands of this field. Finally, we gather the overviewed studies with their available open-source implementations at https://github.com/amirhossein-kz/Awesome-Diffusion-Models-in-Medical-Imaging.

翻译：去噪扩散模型作为一类生成模型，近期在各种深度学习问题中引起了极大兴趣。扩散概率模型定义了一个前向扩散阶段，其中输入数据通过逐步添加高斯噪声而被逐渐扰动，然后学习逆转扩散过程，从噪声数据样本中恢复出所需的无噪声数据。扩散模型因其强大的模式覆盖能力和生成样本的质量而广受赞誉，尽管它们存在已知的计算负担。借助计算机视觉领域的进展，医学成像领域对扩散模型的兴趣也在增长。为帮助研究者驾驭这一繁荣局面，本综述旨在全面概述医学图像分析学科中的扩散模型。具体而言，我们介绍了扩散模型坚实的理论基础和基本概念，以及三种通用的扩散建模框架：扩散概率模型、噪声条件得分网络和随机微分方程。然后，我们提供了医学领域扩散模型的系统分类法，并基于其应用、成像模态、感兴趣器官和算法提出了多视角分类法。为此，我们涵盖了扩散模型在医学领域中的广泛应用程序。此外，我们强调了某些选定方法的实际用例，并进而讨论了扩散模型在医学领域中的局限性，提出了若干方向以满足该领域的需求。最后，我们汇总了所综述的研究及其可用的开源实现，链接为 https://github.com/amirhossein-kz/Awesome-Diffusion-Models-in-Medical-Imaging。