Unsupervised Imaging Inverse Problems with Diffusion Distribution Matching

2025-06-17

AI Summary

This work addresses the blind inverse problem in image restoration under realistic constraints: unknown forward degradation models and absence of paired training data. We propose an unsupervised learning framework requiring only a small set of unpaired degraded and clean images. Methodologically, we introduce the first unified distribution alignment paradigm that jointly learns conditional flow matching and the forward degradation model—enabling end-to-end co-estimation of restored images and spatially varying point spread functions (PSFs) or blur kernels. Our approach leverages flow-matching-based generative modeling combined with a diffusion-inspired distribution matching loss to jointly optimize degradation modeling and image restoration. Experiments demonstrate state-of-the-art performance on non-uniform deblurring, PSF calibration, and blind super-resolution—outperforming existing unsupervised and single-image blind methods. Notably, the method successfully recovers real lens PSFs using a minimal acquisition protocol, validating its practical applicability.

Technology Category

• Machine Learning: Unsupervised & Self-Supervised Learning
• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

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.

Problem

• Solves image restoration without paired datasets or known forward models
• Uses small unpaired data to learn degradation and forward models jointly
• Outperforms existing methods in deblurring and blind super-resolution tasks

Innovation

• Uses conditional flow matching for degraded observations
• Learns forward model via distribution-matching loss
• Operates with minimal unpaired datasets assumptions