Unsupervised Imaging Inverse Problems with Diffusion Distribution Matching

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 mis-specified, 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 timeconsuming experiments and specialized equipment. In contrast, our approach achieves this with minimal data acquisition effort. Code available: https://github.com/inria-thoth/ddm4ip.