Data to 7 Oct 2026

Plug-and-Play Methods Provably Converge with Properly Trained Denoisers

arXiv 1905.05406 ↗First posted 14 May 2019cs.CV eess.IVcited by 197

Not on the map. Why?

Cited by 20 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Plug-and-play (PnP) is a non-convex framework that integrates modern denoising priors, such as BM3D or deep learning-based denoisers, into ADMM or other proximal algorithms. An advantage of PnP is that one can use pre-trained denoisers when there is not sufficient data for end-to-end training. Although PnP has been recently studied extensively with great empirical success, theoretical analysis addressing even the most basic question of convergence has been insufficient. In this paper, we theoretically establish convergence of PnP-FBS and PnP-ADMM, without using diminishing stepsizes, under a certain Lipschitz condition on the denoisers. We then propose real spectral normalization, a technique for training deep learning-based denoisers to satisfy the proposed Lipschitz condition. Finally, we present experimental results validating the theory.

Key facts. Cited by 197 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 May 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 27; 2022: 35; 2023: 40; 2024: 33; 2025: 33; 2026: 29.

197 papers.

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2023Denoising Diffusion Models for Plug-and-Play Image Restorationcited by 335
2021Learning to Optimize: A Primer and A Benchmarkcited by 206
2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
2021Deep Equilibrium Architectures for Inverse Problems in Imagingcited by 126
2022Deep Generalized Unfolding Networks for Image Restorationcited by 119
2021Gradient Step Denoiser for convergent Plug-and-Playcited by 107
2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 96
2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priorscited by 93
2024PnP-Flow: Plug-and-Play Image Restoration with Flow Matchingcited by 92
2022Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularizationcited by 79
2021Skew Orthogonal Convolutionscited by 67
2023Provable Probabilistic Imaging using Score-Based Generative Priorscited by 51

38 more

2022Learned reconstruction methods with convergence guaranteescited by 46
2022Equivariant Hypergraph Diffusion Neural Operatorscited by 45
2021Plug-and-Play Algorithms for Video Snapshot Compressive Imagingcited by 42
2022A Neural-Network-Based Convex Regularizer for Inverse Problemscited by 40
2025Vision-Language Gradient Descent-driven All-in-One Deep Unfolding Networkscited by 37
2021DWDN: Deep Wiener Deconvolution Network for Non-Blind Image Deblurringcited by 36
2023Fast Diffusion EM: a diffusion model for blind inverse problems with application to deconvolutioncited by 36
2023How to estimate carbon footprint when training deep learning models? A guide and reviewcited by 34
2021End-to-end reconstruction meets data-driven regularization for inverse problemscited by 32
2023Equivariant plug-and-play image reconstructioncited by 26
2021Solving Inverse Problems by Joint Posterior Maximization with Autoencoding Priorcited by 24
2021Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithmscited by 24
2023What's in a Prior? Learned Proximal Networks for Inverse Problemscited by 24
2022Improving Lipschitz-Constrained Neural Networks by Learning Activation Functionscited by 23
2021Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Conditioncited by 22
2021NTIRE 2021 Challenge on Burst Super-Resolution: Methods and Resultscited by 22
2022Online Deep Equilibrium Learning for Regularization by Denoisingcited by 22
2022Theoretical Perspectives on Deep Learning Methods in Inverse Problemscited by 22
2022Residual Degradation Learning Unfolding Framework with Mixing Priors across Spectral and Spatial for Compressive Spectral Imagingcited by 22
2021Lucas-Kanade Reloaded: End-to-End Super-Resolution from Raw Image Burstscited by 21
2022WaveFit: An Iterative and Non-autoregressive Neural Vocoder based on Fixed-Point Iterationcited by 20
2021Universal and Flexible Optical Aberration Correction Using Deep-Prior Based Deconvolutioncited by 19
2021Fixed-Point and Objective Convergence of Plug-and-Play Algorithmscited by 19
2022Efficiently Training Low-Curvature Neural Networkscited by 19
2023Efficient Bound of Lipschitz Constant for Convolutional Layers by Gram Iterationcited by 19
2021SGD-Net: Efficient Model-Based Deep Learning with Theoretical Guaranteescited by 18
2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
2024Plug-and-Play image restoration with Stochastic deNOising REgularizationcited by 17
2021Learning local regularization for variational image restorationcited by 16
2022Approximation of Lipschitz Functions using Deep Spline Neural Networkscited by 15
2023Provably Convergent Plug-and-Play Quasi-Newton Methodscited by 15
2022On Maximum-a-Posteriori estimation with Plug & Play priors and stochastic gradient descentcited by 14
2023OTRE: Where Optimal Transport Guided Unpaired Image-to-Image Translation Meets Regularization by Enhancingcited by 14
2023Convergent Bregman Plug-and-Play Image Restoration for Poisson Inverse Problemscited by 14
2021Untrained networks for compressive lensless photographycited by 13
2023Convergent regularization in inverse problems and linear plug-and-play denoiserscited by 13
2023A relaxed proximal gradient descent algorithm for convergent plug-and-play with proximal denoisercited by 12
2022Deep Model-Based Super-Resolution with Non-uniform Blurcited by 10

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