MAP-based Problem-Agnostic diffusion model for Inverse Problems

TL;DR

This paper introduces a problem-agnostic diffusion model using MAP-based guided term estimation, improving inverse problem solutions by better capturing data properties and enhancing content preservation.

Contribution

It proposes a novel MAP-based guided term estimation method that leverages unconditionally pretrained diffusion models for inverse problems.

Findings

Better content preservation in super-resolution tasks

More coherent inpainting results near masked regions

Improved performance over state-of-the-art methods

Abstract

Diffusion models have indeed shown great promise in solving inverse problems in image processing. In this paper, we propose a novel, problem-agnostic diffusion model called the maximum a posteriori (MAP)-based guided term estimation method for inverse problems. To leverage unconditionally pretrained diffusion models to address conditional generation tasks, we divide the conditional score function into two terms according to Bayes' rule: an unconditional score function (approximated by a pretrained score network) and a guided term, which is estimated using a novel MAP-based method that incorporates a Gaussian-type prior of natural images. This innovation allows us to better capture the intrinsic properties of the data, leading to improved performance. Numerical results demonstrate that our method preserves contents more effectively compared to state-of-the-art methods--for example, maintaining the structure of glasses in super-resolution tasks and producing more coherent results in the neighborhood of masked regions during inpainting.