Learning Diffusion Model from Noisy Measurement using Principled Expectation-Maximization Method

TL;DR

This paper introduces a principled EM framework for learning diffusion models directly from noisy and corrupted measurements, enabling high-quality image reconstruction without relying on clean datasets.

Contribution

It presents a novel EM-based method that iteratively estimates clean images and trains diffusion models from noisy data with arbitrary corruption types, with theoretical convergence guarantees.

Findings

Effective learning of diffusion priors from noisy data.

Improved image reconstruction in inverse problems.

Versatile application across various imaging tasks.

Abstract

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.