# Convergent Plug-and-Play Image Restoration with Annealed Noise Levels

arXiv: https://arxiv.org/abs/2609.32393 · HTML: https://mlsanity.com/paper/2609.32393/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 41 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 30 of 31)

- [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)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (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)
- [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)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (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)
- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)
- [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)
- [Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging](https://mlsanity.com/paper/2203.17061/) (2022)
- [Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularization](https://mlsanity.com/paper/2201.13256/) (2022)
- [An Online Plug-and-Play Algorithm for Regularized Image Reconstruction](https://mlsanity.com/paper/1809.04693/) (2018)
- [Scalable Plug-and-Play ADMM with Convergence Guarantees](https://mlsanity.com/paper/2006.03224/) (2020)
- [Provable Convergence of Plug-and-Play Priors with MMSE denoisers](https://mlsanity.com/paper/2005.07685/) (2020)
- [Tuning-free Plug-and-Play Proximal Algorithm for Inverse Imaging Problems](https://mlsanity.com/paper/2002.09611/) (2020)
- [A characterization of proximity operators](https://mlsanity.com/paper/1807.04014/) (2018)
- [DeepInverse: A Python package for solving imaging inverse problems with deep learning](https://mlsanity.com/paper/2505.20160/) (2025)
- [Equivariant plug-and-play image reconstruction](https://mlsanity.com/paper/2312.01831/) (2023)
- [Plug-and-Play image restoration with Stochastic deNOising REgularization](https://mlsanity.com/paper/2402.01779/) (2024)
- [A relaxed proximal gradient descent algorithm for convergent plug-and-play with proximal denoiser](https://mlsanity.com/paper/2301.13731/) (2023)
- [Unifying abstract inexact convergence theorems and block coordinate variable metric iPiano](https://mlsanity.com/paper/1602.07283/) (2016)
- [MAP Estimation with Denoisers: Convergence Rates and Guarantees](https://mlsanity.com/paper/2507.15397/) (2025)
- [Stochastic Generative Plug-and-Play Priors](https://mlsanity.com/paper/2604.03603/) (2026)
- [Taming Score-Based Denoisers in ADMM: A Convergent Plug-and-Play Framework](https://mlsanity.com/paper/2603.10281/) (2026)

## Abstract (arXiv)

Plug-and-Play (PnP) methods solve imaging inverse problems by incorporating deep denoisers into iterative optimization algorithms. Although practical implementations often decrease the denoiser noise level σ along iterations, most existing convergence analyses assume a fixed denoiser. In this work, we establish convergence guarantees for a broad family of Plug-and-Play algorithms with annealed noise level, spanning deterministic methods (RED--GD and PnP--PGD) and stochastic methods (SNORE, equivariant RED, and a variant of PnP--Flow). For each method, we identify an explicit, nonconvex objective associated with the terminal denoising level and prove asymptotic stationarity of the iterates with respect to this objective. Our analysis does not prescribe any decay rate for the noise schedule, and our assumptions cover both learned gradient-step denoisers and exact MMSE denoisers. Overall, our theoretical results bridge the gap between existing PnP convergence theory and the decreasing-denoising practices used by state-of-the-art image restoration methods. We empirically demonstrate the benefits of such schedules and illustrate the predicted convergence behavior on several imaging inverse problems, including inpainting, super-resolution, demosaicing and tomography.