  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.
