基于扩散模型的非配对数据学习用于逆问题
Diffusion Based Unpaired Data Learning for Inverse Problems
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中文总结 AI 辅助
针对非配对数据获取难的逆问题，提出基于扩散模型的LUD-DIF方法，经理论推导与实验验证，该方法在多类图像逆问题中表现优异，具备有效性与泛化性。
中文摘要 AI 辅助
数据在许多基于深度学习的逆问题求解器中至关重要。然而，在许多场景下获取充足的配对数据仍极具挑战性，而非配对数据则成本低廉。为最大化数据利用率，本文提出LUD-DIF，一种基于扩散模型的非配对数据逆问题求解方法。从联合分布的证据下界（ELBO）出发，在弱耦合假设下将其解耦为两个独立的扩散过程。该方法从变分推断视角提供理论支撑，推导损失函数，定量分析该假设引入的误差界，并提供受定理启发的超参数选择启发式策略。实验结果表明，LUD-DIF在多个图像逆问题上表现出色，验证了其在非配对逆问题场景下的有效性与泛化能力。
英文摘要
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.
发表机构
- Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）
- Department of Mathematical Sciences, Tsinghua University（清华大学数学科学系）
- RWTH Aachen University（亚琛工业大学）
- School of Artificial Intelligence, Wuhan University（武汉大学人工智能学院）
- Department of Applied Mathematics, The Hong Kong Polytechnic University（香港理工大学应用数学系）
机构由 AI 辅助整理，请以论文原文为准。
