Original title: Diffusion Based Unpaired Data Learning for Inverse Problems
Chenglong Bao, Yiming Dang, Chenguang Duan, Yuling Jiao +1 · September 2026
Many computer systems solve inverse problemsTasks where you infer hidden causes from observed effects, like reconstructing images from distorted versions., such as reconstructing a clear image from damaged measurements. Teaching these systems usually requires paired dataDataset where each input has a corresponding correct output for training., which means matching every bad input directly to its exact good target. Getting these pairs is hard, but unpaired data is cheap and easy to find. To solve this, researchers built LUD-DIF. It uses diffusion modelsAI models that generate data by gradually denoising random noise into structured outputs., which learn to generate clean data by reversing a gradual noise-adding process. The researchers took the math of how the data connects and split it into two independent diffusion processes by assuming the inputs and outputs are weakly coupled. This allows the system to learn without matched pairs. Tests on multiple image inverse problems showed that LUD-DIF achieves outstanding performance and generalizes well.
Imagine trying to assemble a jigsaw puzzle without knowing which pieces belong together, having only two separate piles of pieces from different boxes. Normally, you'd need matched pairs of pieces to start, but here you have no matches. In this paper, the problem is like solving an image task without paired data, and the method uses two separate sorting processes to eventually align the pieces into a complete picture.
Many fields need paired data for AI to work, but it's often expensive or impossible to get. This method allows using cheaper unpaired data, making solutions more accessible for tasks like medical imaging.
The abstract does not explicitly state limitations, but it implies that the weak-coupling assumption may introduce errors, and the method is validated only on image inverse problems, suggesting possible constraints in generalization to other domains.
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Diffusion Based Unpaired Data Learning for Inverse Problems — Chenglong Bao, Yiming Dang, Chenguang Duan et al.
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.