Title: DiffEM: Learning from Corrupted Data with Diffusion Models via Expectation Maximization
Primary area: generative models
Keywords: diffusion model, expectation maximization, latent model

Abstract: 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 novel method for training diffusion models with Expectation-Maximization (EM) from noisy 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.