Diffusion Based Unpaired Data Learning for Inverse Problems

2026-09-01

AI Summary

本文提出LUD-DIF方法，通过解耦扩散过程利用非配对数据解决逆问题，提供理论支持并优化超参数选择。

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.

Problem

• unpaired data
• inverse problems
• deep learning

Innovation

• Diffusion Process
• Unpaired Data
• Inverse Problems
• Evidence Lower Bound (ELBO)
• Variational Inference