# Unsupervised Imaging Inverse Problems with Diffusion Distribution Matching

arXiv: https://arxiv.org/abs/2506.14605 · HTML: https://mlsanity.com/paper/2506.14605/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 61 references that are in the map.
- First posted on arXiv 17 Jun 2025.

## Builds on (most cited first, 30 of 45)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Real-ESRGAN: Training Real-World Blind Super-Resolution with Pure Synthetic Data](https://mlsanity.com/paper/2107.10833/) (2021)
- [Designing a Practical Degradation Model for Deep Blind Image Super-Resolution](https://mlsanity.com/paper/2103.14006/) (2021)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- ["Zero-Shot" Super-Resolution using Deep Internal Learning](https://mlsanity.com/paper/1712.06087/) (2017)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Models](https://mlsanity.com/paper/2305.18455/) (2023)
- [Blind Super-Resolution With Iterative Kernel Correction](https://mlsanity.com/paper/1904.03377/) (2019)
- [Blind Super-Resolution Kernel Estimation using an Internal-GAN](https://mlsanity.com/paper/1909.06581/) (2019)
- [Defocus Deblurring Using Dual-Pixel Data](https://mlsanity.com/paper/2005.00305/) (2020)
- [Unsupervised Image Super-Resolution using Cycle-in-Cycle Generative Adversarial Networks](https://mlsanity.com/paper/1809.00437/) (2018)
- [Neural Blind Deconvolution Using Deep Priors](https://mlsanity.com/paper/1908.02197/) (2019)
- [Parallel Diffusion Models of Operator and Image for Blind Inverse Problems](https://mlsanity.com/paper/2211.10656/) (2022)
- [To learn image super-resolution, use a GAN to learn how to do image degradation first](https://mlsanity.com/paper/1807.11458/) (2018)
- [Iterative Filter Adaptive Network for Single Image Defocus Deblurring](https://mlsanity.com/paper/2108.13610/) (2021)
- [NTIRE 2020 Challenge on Real-World Image Super-Resolution: Methods and Results](https://mlsanity.com/paper/2005.01996/) (2020)
- [Flow-based Kernel Prior with Application to Blind Super-Resolution](https://mlsanity.com/paper/2103.15977/) (2021)
- [Unpaired Image Super-Resolution using Pseudo-Supervision](https://mlsanity.com/paper/2002.11397/) (2020)
- [Unsupervised Learning for Real-World Super-Resolution](https://mlsanity.com/paper/1909.09629/) (2019)
- [GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration](https://mlsanity.com/paper/2301.12686/) (2023)

## Built on by (most cited first, 5 of 5)

- [Generative Modeling from Black-box Corruptions via Self-Consistent Stochastic Interpolants](https://mlsanity.com/paper/2512.10857/) (2025)
- [Beyond Fixed Inference: Quantitative Flow Matching for Adaptive Image Denoising](https://mlsanity.com/paper/2604.02392/) (2026)
- [Diffusion Based Unpaired Data Learning for Inverse Problems](https://mlsanity.com/paper/2609.01370/) (2026)
- [When Unpaired Sets Support Shared-Corruption Calibration: Moment Geometry and Two-Sample Precision](https://mlsanity.com/paper/2609.26209/) (2026)
- [ASTRA-SR: Atmospheric Seeing and Turbulence Restoration for Astronomical Image Super-Resolution](https://mlsanity.com/paper/2609.26731/) (2026)

## Abstract (arXiv)

This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches -- which typically assume full knowledge of the forward model or access to paired degraded and ground-truth images -- the proposed method operates under minimal assumptions and relies only on small, unpaired datasets. This makes it particularly well-suited for real-world scenarios, where the forward model is often unknown or misspecified, and collecting paired data is costly or infeasible. The method leverages conditional flow matching to model the distribution of degraded observations, while simultaneously learning the forward model via a distribution-matching loss that arises naturally from the framework. Empirically, it outperforms both single-image blind and unsupervised approaches on deblurring and non-uniform point spread function (PSF) calibration tasks. It also matches state-of-the-art performance on blind super-resolution. We also showcase the effectiveness of our method with a proof of concept for lens calibration: a real-world application traditionally requiring time-consuming experiments and specialized equipment. In contrast, our approach achieves this with minimal data acquisition effort.