# Deep Unfolding with Normalizing Flow Priors for Inverse Problems

arXiv: https://arxiv.org/abs/2107.02848 · HTML: https://mlsanity.com/paper/2107.02848/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2021.

## Built on by (most cited first, 23 of 23)

- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [PnP-Flow: Plug-and-Play Image Restoration with Flow Matching](https://mlsanity.com/paper/2410.02423/) (2024)
- [Monte Carlo guided Diffusion for Bayesian linear inverse problems](https://mlsanity.com/paper/2308.07983/) (2023)
- [PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularization](https://mlsanity.com/paper/2205.12021/) (2022)
- [Learning Regularization Functionals for Inverse Problems: A Comparative Study](https://mlsanity.com/paper/2510.01755/) (2025)
- [Removing Structured Noise with Diffusion Models](https://mlsanity.com/paper/2302.05290/) (2023)
- [RPCANet++: Deep Interpretable Robust PCA for Sparse Object Segmentation](https://mlsanity.com/paper/2508.04190/) (2025)
- [Robust Stochastically-Descending Unrolled Networks](https://mlsanity.com/paper/2312.15788/) (2023)
- [Unsupervised Learning of Sampling Distributions for Particle Filters](https://mlsanity.com/paper/2302.01174/) (2023)
- [BlindHarmony: "Blind" Harmonization for MR Images via Flow model](https://mlsanity.com/paper/2305.10732/) (2023)
- [Ultrasound Speckle Suppression and Denoising using MRI-derived Normalizing Flow Priors](https://mlsanity.com/paper/2112.13110/) (2021)
- [Bayesian ECG reconstruction using denoising diffusion generative models](https://mlsanity.com/paper/2401.05388/) (2023)
- [Poisson-Gaussian Holographic Phase Retrieval with Score-based Image Prior](https://mlsanity.com/paper/2305.07712/) (2023)
- [Adaptation of the super resolution SOTA for Art Restoration in camera capture images](https://mlsanity.com/paper/2309.13655/) (2023)
- [Moir'eXNet: Adaptive Multi-Scale Demoir'eing with Linear Attention Test-Time Training and Truncated Flow Matching Prior](https://mlsanity.com/paper/2506.15929/) (2025)
- [SP3: Spherical Priors for Plug-and-Play Restoration](https://mlsanity.com/paper/2606.16396/) (2026)
- [Compressed Sensing of Generative Sparse-latent (GSL) Signals](https://mlsanity.com/paper/2310.15119/) (2023)
- [Unsupervised Low-dose CT Reconstruction with One-way Conditional Normalizing Flows](https://mlsanity.com/paper/2410.17543/) (2024)
- [How to warm-start your unfolding network](https://mlsanity.com/paper/2502.01854/) (2025)
- [Robust Non-negative Proximal Gradient Algorithm for Inverse Problems](https://mlsanity.com/paper/2510.23362/) (2025)
- [Unrolled Neural Networks for Constrained Optimization](https://mlsanity.com/paper/2601.17274/) (2026)
- [Recovering Weak Signals with Normalizing Flows](https://mlsanity.com/paper/2609.06382/) (2026)
- [Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding](https://mlsanity.com/paper/2609.30539/) (2026)

## Abstract (arXiv)

Many application domains, spanning from computational photography to medical imaging, require recovery of high-fidelity images from noisy, incomplete or partial/compressed measurements. State of the art methods for solving these inverse problems combine deep learning with iterative model-based solvers, a concept known as deep algorithm unfolding. By combining a-priori knowledge of the forward measurement model with learned (proximal) mappings based on deep networks, these methods yield solutions that are both physically feasible (data-consistent) and perceptually plausible. However, current proximal mappings only implicitly learn such image priors. In this paper, we propose to make these image priors fully explicit by embedding deep generative models in the form of normalizing flows within the unfolded proximal gradient algorithm. We demonstrate that the proposed method outperforms competitive baselines on various image recovery tasks, spanning from image denoising to inpainting and deblurring.