Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems

TL;DR

This paper introduces DMPS, a fast and effective method for noisy linear inverse problems using diffusion and flow-based models, achieving competitive or superior results with reduced inference time.

Contribution

It proposes a simple closed-form approximation to the likelihood score, significantly speeding up inference in diffusion-based inverse problem solutions.

Findings

DMPS outperforms baseline methods in reconstruction quality.

DMPS significantly reduces inference time.

Applicable to various inverse problems like super-resolution and deblurring.

Abstract

With the rapid development of diffusion models and flow-based generative models, there has been a surge of interests in solving noisy linear inverse problems, e.g., super-resolution, deblurring, denoising, colorization, etc, with generative models. However, while remarkable reconstruction performances have been achieved, their inference time is typically too slow since most of them rely on the seminal diffusion posterior sampling (DPS) framework and thus to approximate the intractable likelihood score, time-consuming gradient calculation through back-propagation is needed. To address this issue, this paper provides a fast and effective solution by proposing a simple closed-form approximation to the likelihood score. For both diffusion and flow-based models, extensive experiments are conducted on various noisy linear inverse problems such as noisy super-resolution, denoising, deblurring, and colorization. In all these tasks, our method (namely DMPS) demonstrates highly competitive or even better reconstruction performances while being significantly faster than all the baseline methods.