Diffusion model is a class of generative models that learns the gradient of the unnormalized log prior density. Diffusion models are easy to train, as the training amounts to training a denoiser on multiple noise levels. Equipped with a powerful generative prior that is modeled with a diffusion model, one can solve inverse problems through posterior sampling, leveraging the principles of Bayesian inference. In this chapter, we review the principles of diffusion models and study how they can be used to solve inverse problems that arise in medical imaging, focusing on MRI and CT reconstruction tasks.