Diffusion models have emerged as powerful generative priors for high-dimensional inverse problems, yet learning them when only corrupted or noisy observations are available remains challenging. In this work, we propose a new method for training diffusion models with Expectation-Maximization (EM) from corrupted data. Our proposed method, DiffEM, utilizes conditional diffusion models to reconstruct clean data from observations in the E-step, and then uses the reconstructed data to refine the conditional diffusion model in the M-step. Theoretically, we provide monotonic convergence guarantees for the DiffEM iteration, assuming appropriate statistical conditions. We demonstrate the effectiveness of our approach through experiments on various image reconstruction tasks.
@article{arxiv.2510.12691,
title = {DiffEM: Learning from Corrupted Data with Diffusion Models via Expectation Maximization},
author = {Danial Hosseintabar and Fan Chen and Giannis Daras and Antonio Torralba and Constantinos Daskalakis},
journal= {arXiv preprint arXiv:2510.12691},
year = {2025}
}