# Plug-and-Play Posterior Sampling under Mismatched Measurement and Prior Models

arXiv: https://arxiv.org/abs/2310.03546 · HTML: https://mlsanity.com/paper/2310.03546/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 45 references that are in the map.
- First posted on arXiv 5 Oct 2023.

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

- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [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)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)
- [Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions](https://mlsanity.com/paper/2211.01916/) (2022)
- [Theoretical guarantees for approximate sampling from smooth and log-concave densities](https://mlsanity.com/paper/1412.7392/) (2014)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration](https://mlsanity.com/paper/2303.11435/) (2023)
- [Adaptive Diffusion Priors for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.05876/) (2022)
- [Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie](https://mlsanity.com/paper/2103.04715/) (2021)
- [NETT: Solving Inverse Problems with Deep Neural Networks](https://mlsanity.com/paper/1803.00092/) (2018)
- [Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau](https://mlsanity.com/paper/1612.07471/) (2016)
- [A Review of Convolutional Neural Networks for Inverse Problems in Imaging](https://mlsanity.com/paper/1710.04011/) (2017)
- [Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularization](https://mlsanity.com/paper/2201.13256/) (2022)
- [DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstruction](https://mlsanity.com/paper/2211.12340/) (2022)
- [Conditional Simulation Using Diffusion Schr"odinger Bridges](https://mlsanity.com/paper/2202.13460/) (2022)
- [prDeep: Robust Phase Retrieval with a Flexible Deep Network](https://mlsanity.com/paper/1803.00212/) (2018)
- [RxRx1: A Dataset for Evaluating Experimental Batch Correction Methods](https://mlsanity.com/paper/2301.05768/) (2023)
- [Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inference](https://mlsanity.com/paper/2304.11134/) (2023)
- [Provable Convergence of Plug-and-Play Priors with MMSE denoisers](https://mlsanity.com/paper/2005.07685/) (2020)
- [Principal Uncertainty Quantification with Spatial Correlation for Image Restoration Problems](https://mlsanity.com/paper/2305.10124/) (2023)
- [Generative Plug and Play: Posterior Sampling for Inverse Problems](https://mlsanity.com/paper/2306.07233/) (2023)
- [SIMBA: Scalable Inversion in Optical Tomography using Deep Denoising Priors](https://mlsanity.com/paper/1911.13241/) (2019)

## Built on by (most cited first, 8 of 8)

- [Deep Diffusion Image Prior for Efficient OOD Adaptation in 3D Inverse Problems](https://mlsanity.com/paper/2407.10641/) (2024)
- [Plug-and-Play image restoration with Stochastic deNOising REgularization](https://mlsanity.com/paper/2402.01779/) (2024)
- [DGSolver: Diffusion Generalist Solver with Universal Posterior Sampling for Image Restoration](https://mlsanity.com/paper/2504.21487/) (2025)
- [Efficient Bayesian Computation Using Plug-and-Play Priors for Poisson Inverse Problems](https://mlsanity.com/paper/2503.16222/) (2025)
- [DC-LA: Difference-of-Convex Langevin Algorithm](https://mlsanity.com/paper/2601.22932/) (2026)
- [Outlier-robust Diffusion Posterior Sampling for Bayesian Inverse Problems](https://mlsanity.com/paper/2602.02045/) (2026)
- [Vis-CoT: A Human-in-the-Loop Framework for Interactive Visualization and Intervention in LLM Chain-of-Thought Reasoning](https://mlsanity.com/paper/2509.01412/) (2025)
- [Bregman geometry-aware split Gibbs sampling for Bayesian Poisson inverse problems](https://mlsanity.com/paper/2511.12257/) (2025)

## Abstract (arXiv)

Posterior sampling has been shown to be a powerful Bayesian approach for solving imaging inverse problems. The recent plug-and-play unadjusted Langevin algorithm (PnP-ULA) has emerged as a promising method for Monte Carlo sampling and minimum mean squared error (MMSE) estimation by combining physical measurement models with deep-learning priors specified using image denoisers. However, the intricate relationship between the sampling distribution of PnP-ULA and the mismatched data-fidelity and denoiser has not been theoretically analyzed. We address this gap by proposing a posterior-L2 pseudometric and using it to quantify an explicit error bound for PnP-ULA under mismatched posterior distribution. We numerically validate our theory on several inverse problems such as sampling from Gaussian mixture models and image deblurring. Our results suggest that the sensitivity of the sampling distribution of PnP-ULA to a mismatch in the measurement model and the denoiser can be precisely characterized.