Unsupervised Imaging Inverse Problems with Diffusion Distribution Matching
Journal:
arXiv
Published Date:
Jun 17, 2025
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.
