# Diff-Unfolding: A Model-Based Score Learning Framework for Inverse Problems

arXiv: https://arxiv.org/abs/2505.11393 · HTML: https://mlsanity.com/paper/2505.11393/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 37 of its 51 references that are in the map.
- First posted on arXiv 16 May 2025.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 30 of 37)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Models](https://mlsanity.com/paper/2104.14951/) (2021)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Residual Non-local Attention Networks for Image Restoration](https://mlsanity.com/paper/1903.10082/) (2019)
- [CycleISP: Real Image Restoration via Improved Data Synthesis](https://mlsanity.com/paper/2003.07761/) (2020)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems](https://mlsanity.com/paper/2303.05754/) (2023)
- [Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors](https://mlsanity.com/paper/2405.18782/) (2024)
- [Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion](https://mlsanity.com/paper/2312.00852/) (2023)

## Built on by (most cited first, 3 of 3)

- [MRI Super-Resolution with Deep Learning: A Comprehensive Survey](https://mlsanity.com/paper/2511.16854/) (2025)
- [Learning few-step posterior samplers by unfolding and distillation of diffusion models](https://mlsanity.com/paper/2507.02686/) (2025)
- [Automated Tuning for Diffusion Inverse Problem Solvers without Generative Prior Retraining](https://mlsanity.com/paper/2509.09880/) (2025)

## Abstract (arXiv)

Diffusion models are extensively used for modeling image priors for inverse problems. We introduce Diff-Unfolding, a principled framework for learning posterior score functions of conditional diffusion models by explicitly incorporating the physical measurement operator into a modular network architecture. Diff-Unfolding formulates posterior score learning as the training of an unrolled optimization scheme, where the measurement model is decoupled from the learned image prior. This design allows our method to generalize across inverse problems at inference time by simply replacing the forward operator without retraining. We theoretically justify our unrolling approach by showing that the posterior score can be derived from a composite model-based optimization formulation. Extensive experiments on image restoration and accelerated MRI show that Diff-Unfolding achieves state-of-the-art performance, improving PSNR by up to 2 dB and reducing LPIPS by 22.7%, while being both compact (47M parameters) and efficient (0.72 seconds per 256 × 256 image). An optimized C++/LibTorch implementation further reduces inference time to 0.63 seconds, underscoring the practicality of our approach.