DiffEM: Learning from Corrupted Data with Diffusion Models via Expectation Maximization
This addresses a challenge in generative modeling for high-dimensional inverse problems, though it appears incremental as it builds on existing diffusion model frameworks.
The paper tackles the problem of training diffusion models when only corrupted or noisy observations are available, proposing DiffEM, a method that uses Expectation-Maximization with conditional diffusion models to reconstruct clean data and refine the model, achieving effectiveness in image reconstruction tasks.
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.