  Diffusion models excel in solving imaging inverse problems due to their
ability to model complex image priors. However, their reliance on large, clean
datasets for training limits their practical use where clean data is scarce. In
this paper, we propose EMDiffusion, an expectation-maximization (EM) approach
to train diffusion models from corrupted observations. Our method alternates
between reconstructing clean images from corrupted data using a known diffusion
model (E-step) and refining diffusion model weights based on these
reconstructions (M-step). This iterative process leads the learned diffusion
model to gradually converge to the true clean data distribution. We validate
our method through extensive experiments on diverse computational imaging
tasks, including random inpainting, denoising, and deblurring, achieving new
state-of-the-art performance.
