Diffusion models have demonstrated exceptional ability in modeling complex image distributions, making them versatile plug-and-play priors for solving imaging inverse problems. However, their reliance on large-scale clean datasets for training limits their applicability in scenarios where acquiring clean data is costly or impractical. Recent approaches have attempted to learn diffusion models directly from corrupted measurements, but these methods either lack theoretical convergence guarantees or are restricted to specific types of data corruption. In this paper, we propose a principled expectation-maximization (EM) framework that iteratively learns diffusion models from noisy data with arbitrary corruption types. Our framework employs a plug-and-play Monte Carlo method to accurately estimate clean images from noisy measurements, followed by training the diffusion model using the reconstructed images. This process alternates between estimation and training until convergence. We evaluate the performance of our method across various imaging tasks, including inpainting, denoising, and deblurring. Experimental results demonstrate that our approach enables the learning of high-fidelity diffusion priors from noisy data, significantly enhancing reconstruction quality in imaging inverse problems.

本研究解决了在获取清晰数据成本高或不切实际的情况下，扩散模型训练的局限性。提出了一种基于原则期望最大化的框架，通过迭代学习来自任意类型噪声数据的扩散模型，显著提升了图像重建质量。实验结果显示，该方法在图像逆问题中，实现了高保真度扩散先验的有效学习。

利用原则期望最大化方法从噪声测量中学习扩散模型