# Integrating Reweighted Least Squares with Plug-and-Play Diffusion Priors for Noisy Image Restoration

arXiv: https://arxiv.org/abs/2511.06823 · HTML: https://mlsanity.com/paper/2511.06823/

## Key facts

- Cited by 1 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 22 of its 47 references that are in the map.
- First posted on arXiv 10 Nov 2025.

## Placed in

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

## Builds on (most cited first, 22 of 22)

- [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)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [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)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems](https://mlsanity.com/paper/1704.03488/) (2017)
- [Regularization by Denoising: Clarifications and New Interpretations](https://mlsanity.com/paper/1806.02296/) (2018)
- [PnP-Flow: Plug-and-Play Image Restoration with Flow Matching](https://mlsanity.com/paper/2410.02423/) (2024)
- [Neumann Networks for Inverse Problems in Imaging](https://mlsanity.com/paper/1901.03707/) (2019)
- [Iterative Reweighted Least Squares Networks With Convergence Guarantees for Solving Inverse Imaging Problems](https://mlsanity.com/paper/2308.05745/) (2023)

## Built on by (most cited first, 1 of 1)

- [Outlier-Robust Diffusion Solvers for Inverse Problems](https://mlsanity.com/paper/2605.09477/) (2026)

## Abstract (arXiv)

Existing plug-and-play image restoration methods typically employ off-the-shelf Gaussian denoisers as proximal operators within classical optimization frameworks based on variable splitting. Recently, denoisers induced by generative priors have been successfully integrated into regularized optimization methods for image restoration under Gaussian noise. However, their application to non-Gaussian noise--such as impulse noise--remains largely unexplored. In this paper, we propose a plug-and-play image restoration framework based on generative diffusion priors for robust removal of general noise types, including impulse noise. Within the maximum a posteriori (MAP) estimation framework, the data fidelity term is adapted to the specific noise model. Departing from the conventional least-squares loss used for Gaussian noise, we introduce a generalized Gaussian scale mixture-based loss, which approximates a wide range of noise distributions and leads to an ℓq-norm (0<q≤2) fidelity term. This optimization problem is addressed using an iteratively reweighted least squares (IRLS) approach, wherein the proximal step involving the generative prior is efficiently performed via a diffusion-based denoiser. Experimental results on benchmark datasets demonstrate that the proposed method effectively removes non-Gaussian impulse noise and achieves superior restoration performance.