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

Weimin Bai, Weiheng Tang, Enze Ye, Siyi Chen, Wenzheng Chen, He Sun

TL;DR

Experimental results demonstrate that the proposed principled expectation-maximization framework enables the learning of high-fidelity diffusion priors from noisy data, significantly enhancing reconstruction quality in imaging inverse problems.

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.

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

TL;DR

Experimental results demonstrate that the proposed principled expectation-maximization framework enables the learning of high-fidelity diffusion priors from noisy data, significantly enhancing reconstruction quality in imaging inverse problems.

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.

Paper Structure

This paper contains 12 sections, 8 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methodology
  3. Preliminaries
  4. Principled Expectation-Maximum Framework
  5. E-step, principled DM-based posterior sampling
  6. M-step, refining diffusion priors
  7. Initialization of the EM iterations
  8. Experiments
  9. Experimental Settings
  10. Image Reconstruction
  11. Learned Diffusion Priors
  12. Conclusion

Figures (3)

  • Figure 1: Qualitive results of image reconstruction on (a) CIFAR-10 noisy measurements and (b) CIFAR-10 masked measurements.
  • Figure 2: Qualitive results on CelebA deblurring. For each image, the blur kernel is a $9\times9$ Gaussian blur kernel. Within the principled iterative learning framework, the diffusion model learns cleaner score-based priors, improving the quality of reconstructed images.
  • Figure 3: Comparison of uncurated samples generated from diffusion models trained by EMDiffusion and the proposed method.