# Diffusion Based Unpaired Data Learning for Inverse Problems

arXiv: https://arxiv.org/abs/2609.01370 · HTML: https://mlsanity.com/paper/2609.01370/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 46 references that are in the map.
- First posted on arXiv 1 Sep 2026.

## Builds on (most cited first, 30 of 30)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019)
- [Toward Convolutional Blind Denoising of Real Photographs](https://mlsanity.com/paper/1807.04686/) (2018)
- [Unprocessing Images for Learned Raw Denoising](https://mlsanity.com/paper/1811.11127/) (2018)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Frequency Separation for Real-World Super-Resolution](https://mlsanity.com/paper/1911.07850/) (2019)
- [Unpaired Image-to-Image Translation via Neural Schr"odinger Bridge](https://mlsanity.com/paper/2305.15086/) (2023)
- [AP-BSN: Self-Supervised Denoising for Real-World Images via Asymmetric PD and Blind-Spot Network](https://mlsanity.com/paper/2203.11799/) (2022)
- [Unsupervised Real-world Image Super Resolution via Domain-distance Aware Training](https://mlsanity.com/paper/2004.01178/) (2020)
- [C2N: Practical Generative Noise Modeling for Real-World Denoising](https://mlsanity.com/paper/2202.09533/) (2022)
- [Towards Realistic Data Generation for Real-World Super-Resolution](https://mlsanity.com/paper/2406.07255/) (2024)
- [Schr"odinger Bridge Flow for Unpaired Data Translation](https://mlsanity.com/paper/2409.09347/) (2024)
- [CVF-SID: Cyclic multi-Variate Function for Self-Supervised Image Denoising by Disentangling Noise from Image](https://mlsanity.com/paper/2203.13009/) (2022)
- [Random Sub-Samples Generation for Self-Supervised Real Image Denoising](https://mlsanity.com/paper/2307.16825/) (2023)
- [DeFlow: Learning Complex Image Degradations from Unpaired Data with Conditional Flows](https://mlsanity.com/paper/2101.05796/) (2021)
- [Unsupervised Image Denoising in Real-World Scenarios via Self-Collaboration Parallel Generative Adversarial Branches](https://mlsanity.com/paper/2308.06776/) (2023)
- [Optimal low-rank approximations of Bayesian linear inverse problems](https://mlsanity.com/paper/1407.3463/) (2014)
- [Asymmetric GAN for Unpaired Image-to-image Translation](https://mlsanity.com/paper/1912.11660/) (2019)
- [Near-Exact Recovery for Tomographic Inverse Problems via Deep Learning](https://mlsanity.com/paper/2206.07050/) (2022)
- [Optimal Transport-Guided Conditional Score-Based Diffusion Models](https://mlsanity.com/paper/2311.01226/) (2023)
- [Unsupervised Imaging Inverse Problems with Diffusion Distribution Matching](https://mlsanity.com/paper/2506.14605/) (2025)
- [Decoupled Residual Denoising Diffusion Models for Unified and Data Efficient Image-to-Image Translation](https://mlsanity.com/paper/2606.01048/) (2026)
- [Learned Lightweight Smartphone ISP with Unpaired Data](https://mlsanity.com/paper/2505.10420/) (2025)

## Abstract (arXiv)

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.