mlsanityData to 7 Oct 2026

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

arXiv 2310.03546 ↗First posted 5 Oct 2023stat.ML cs.LGcited by 8

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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.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 31 of its 45 references that are in the map. First posted on arXiv 5 Oct 2023.

Builds on

31 of 45 references.

References · 31

  1. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  2. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  3. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  4. 2020Training Generative Adversarial Networks with Limited Datacited by 1,184
  5. 2022Denoising Diffusion Restoration Modelscited by 951
  6. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  7. 2020Plug-and-Play Image Restoration with Deep Denoiser Priorcited by 467
  8. 2016Deep Convolutional Neural Network for Inverse Problems in Imagingcited by 431
  9. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 303
  10. 2020Deep Learning Techniques for Inverse Problems in Imagingcited by 290
  11. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localizationcited by 230
  12. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptionscited by 215
19 more
  1. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 206
  2. 2019Plug-and-Play Methods Provably Converge with Properly Trained Denoiserscited by 197
  3. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restorationcited by 164
  4. 2022Adaptive Diffusion Priors for Accelerated MRI Reconstructioncited by 117
  5. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 96
  6. 2018NETT: Solving Inverse Problems with Deep Neural Networkscited by 89
  7. 2016Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreaucited by 83
  8. 2017A Review of Convolutional Neural Networks for Inverse Problems in Imagingcited by 81
  9. 2022Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularizationcited by 79
  10. 2022DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstructioncited by 73
  11. 2022Conditional Simulation Using Diffusion Schr"odinger Bridgescited by 58
  12. 2018prDeep: Robust Phase Retrieval with a Flexible Deep Networkcited by 46
  13. 2023RxRx1: A Dataset for Evaluating Experimental Batch Correction Methodscited by 45
  14. 2023Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inferencecited by 41
  15. 2020Provable Convergence of Plug-and-Play Priors with MMSE denoiserscited by 39
  16. 2023Principal Uncertainty Quantification with Spatial Correlation for Image Restoration Problemscited by 28
  17. 2023Generative Plug and Play: Posterior Sampling for Inverse Problemscited by 24
  18. 2019SIMBA: Scalable Inversion in Optical Tomography using Deep Denoising Priorscited by 16
  19. 2023Accelerated Bayesian imaging by relaxed proximal-point Langevin samplingcited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 4; 2026: 2.

8 papers.

  1. 2024Deep Diffusion Image Prior for Efficient OOD Adaptation in 3D Inverse Problemscited by 21
  2. 2024Plug-and-Play image restoration with Stochastic deNOising REgularizationcited by 17
  3. 2025DGSolver: Diffusion Generalist Solver with Universal Posterior Sampling for Image Restorationcited by 5
  4. 2025Efficient Bayesian Computation Using Plug-and-Play Priors for Poisson Inverse Problemscited by 2
  5. 2026DC-LA: Difference-of-Convex Langevin Algorithmcited by 1
  6. 2026Outlier-robust Diffusion Posterior Sampling for Bayesian Inverse Problemscited by 1
  7. 2025Vis-CoT: A Human-in-the-Loop Framework for Interactive Visualization and Intervention in LLM Chain-of-Thought Reasoningcited by 0
  8. 2025Bregman geometry-aware split Gibbs sampling for Bayesian Poisson inverse problemscited by 0