Diffusion Based Unpaired Data Learning for Inverse Problems

arXiv (Cornell University)

Abstract

Data is important in many deep learning-based inverse problem solvers. However, obtaining sufficient paired data in many scenarios remains highly challenging, while unpaired data is cheap. To maximize data utilization, this paper proposes LUD-DIF, a diffusion-based approach for solving inverse problems with unpaired data. Starting from the evidence lower bound (ELBO) of the joint distribution, we decouple it into two independent diffusion processes under the weak-coupling assumption. The method provides theoretical support from a variational inference perspective, derives the loss function, quantitatively analyzes the error bound introduced by the assumption, and offers a theorem-motivated heuristic for hyperparameter selection. Experimental results demonstrate that LUD-DIF achieves outstanding performance on multiple image inverse problems, validating its effectiveness and generalization capability in unpaired inverse problem settings.

Authors 5

1. Chenglong Bao

   Tsinghua University

   Affiliation as printed

   Yau Mathematical Sciences Center , Tsinghua University , Beijing , China

2. Yiming Dang

   Tsinghua University

   Affiliation as printed

   Department of Mathematical Sciences , Tsinghua University , Beijing , China

3. Chenguang Duan Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik , RWTH Aachen University , Aachen , Germany

4. Yuling Jiao

   Wuhan University · Wuhan Business University

   Affiliation as printed

   School of Artificial Intelligence , Wuhan University , Wuhan , Hubei , China

5. Defeng Sun

   Hong Kong Polytechnic University

   Affiliation as printed

   Department of Applied Mathematics , The Hong Kong Polytechnic University , Hong Kong , China