Unsupervised Imaging Inverse Problems with Diffusion Distribution Matching

TL;DR

This paper introduces an unsupervised image restoration method that operates with unpaired datasets and minimal assumptions, effectively handling real-world inverse problems like deblurring and super-resolution without needing paired data or full knowledge of the forward model.

Contribution

It presents a novel approach using diffusion distribution matching for inverse problems, enabling effective image restoration with unpaired data and minimal prior knowledge, outperforming existing methods.

Findings

Outperforms single-image blind and unsupervised methods on deblurring and PSF calibration.

Matches state-of-the-art on blind super-resolution.

Successfully applied to real-world lens calibration with minimal data.

Abstract

This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches -- which typically assume full knowledge of the forward model or access to paired degraded and ground-truth images -- the proposed method operates under minimal assumptions and relies only on small, unpaired datasets. This makes it particularly well-suited for real-world scenarios, where the forward model is often unknown or misspecified, and collecting paired data is costly or infeasible. The method leverages conditional flow matching to model the distribution of degraded observations, while simultaneously learning the forward model via a distribution-matching loss that arises naturally from the framework. Empirically, it outperforms both single-image blind and unsupervised approaches on deblurring and non-uniform point spread function (PSF) calibration tasks. It also matches state-of-the-art performance on blind super-resolution. We also showcase the effectiveness of our method with a proof of concept for lens calibration: a real-world application traditionally requiring time-consuming experiments and specialized equipment. In contrast, our approach achieves this with minimal data acquisition effort.