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.

翻译：扩散模型已成为解决高维逆问题的强大生成先验，但在仅能获取含噪或损坏观测数据时，其训练仍具挑战性。本研究提出一种基于期望最大化（EM）的扩散模型训练方法，用于处理含噪数据。所提出的DiffEM方法在E步中利用条件扩散模型从观测数据重建干净数据，随后在M步中使用重建数据优化条件扩散模型。理论上，我们在适当的统计条件下为DiffEM迭代提供了单调收敛性保证。通过在多种图像重建任务上的实验，验证了该方法的有效性。