mlsanityData to 14 Oct 2026

Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inference

arXiv 2304.11134 ↗First posted 21 Apr 2023stat.ML cs.CV cs.LGcited by 42

Not on the map. Why?

Cited by 29 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

This paper introduces a stochastic plug-and-play (PnP) sampling algorithm that leverages variable splitting to efficiently sample from a posterior distribution. The algorithm based on split Gibbs sampling (SGS) draws inspiration from the alternating direction method of multipliers (ADMM). It divides the challenging task of posterior sampling into two simpler sampling problems. The first problem depends on the likelihood function, while the second is interpreted as a Bayesian denoising problem that can be readily carried out by a deep generative model. Specifically, for an illustrative purpose, the proposed method is implemented in this paper using state-of-the-art diffusion-based generative models. Akin to its deterministic PnP-based counterparts, the proposed method exhibits the great advantage of not requiring an explicit choice of the prior distribution, which is rather encoded into a pre-trained generative model. However, unlike optimization methods (e.g., PnP-ADMM) which generally provide only point estimates, the proposed approach allows conventional Bayesian estimators to be accompanied by confidence intervals at a reasonable additional computational cost. Experiments on commonly studied image processing problems illustrate the efficiency of the proposed sampling strategy. Its performance is compared to recent state-of-the-art optimization and sampling methods.

Key facts. Cited by 42 papers in the map (data through 14 Oct 2026). Builds on 29 of its 51 references that are in the map. First posted on arXiv 21 Apr 2023.

Builds on

29 of 51 references.

References · 29

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  3. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  5. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 6,013
  6. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  7. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
  8. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,416
  9. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,358
  10. 2021Variational Diffusion Modelscited by 1,153
  11. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,043
  12. 2022Denoising Diffusion Restoration Modelscited by 963
17 more
  1. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 635
  2. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 521
  3. 2017FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoisingcited by 510
  4. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraintscited by 508
  5. 2020Plug-and-Play Image Restoration with Deep Denoiser Priorcited by 470
  6. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contractioncited by 307
  7. 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 246
  8. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matchingcited by 183
  9. 2018DeepISP: Towards Learning an End-to-End Image Processing Pipelinecited by 88
  10. 2019Plug and play methods for magnetic resonance imaging (long version)cited by 75
  11. 2018Split-and-augmented Gibbs sampler - Application to large-scale inference problemscited by 47
  12. 2015Denoising Criterion for Variational Auto-Encoding Frameworkcited by 43
  13. 2018Scalable Bayesian uncertainty quantification in imaging inverse problems via convex optimizationcited by 22
  14. 2019Efficient MCMC Sampling with Dimension-Free Convergence Rate using ADMM-type Splittingcited by 22
  15. 2017Uncertainty quantification for radio interferometric imaging: I. proximal MCMC methodscited by 13
  16. 2016Maximum-a-posteriori estimation with Bayesian confidence regionscited by 10
  17. 2019Asymptotically exact data augmentation: models, properties and algorithmscited by 8

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 3; 2025: 18; 2026: 18.

42 papers.

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  1. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstructioncited by 73
  2. 2023Provable Probabilistic Imaging using Score-Based Generative Priorscited by 51
  3. 2025Diffusion Tree Sampling: Scalable inference-time alignment of diffusion modelscited by 34
  4. 2025Split Gibbs Discrete Diffusion Posterior Samplingcited by 18
  5. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  6. 2024Plug-and-Play image restoration with Stochastic deNOising REgularizationcited by 17
  7. 2025LATINO-PRO: LAtent consisTency INverse sOlver with PRompt Optimizationcited by 16
  8. 2023Plug-and-Play Posterior Sampling under Mismatched Measurement and Prior Modelscited by 8
  9. 2024Empirical Bayesian image restoration by Langevin sampling with a denoising diffusion implicit priorcited by 6
  10. 2025Strictly Constrained Generative Modeling via Split Augmented Langevin Samplingcited by 6
  11. 2025Learning few-step posterior samplers by unfolding and distillation of diffusion modelscited by 6
  12. 2025Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priorscited by 5
30 more
  1. 2023Variational Bayes image restoration with compressive autoencoderscited by 4
  2. 2025Multitask Learning with Stochastic Interpolantscited by 3
  3. 2025PSI3D: Plug-and-Play 3D Stochastic Inference with Slice-wise Latent Diffusion Priorcited by 3
  4. 2026Sample-efficient evidence estimation of score based priors for model selectioncited by 3
  5. 2026Stochastic Generative Plug-and-Play Priorscited by 3
  6. 2026SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogatecited by 3
  7. 2025Efficient Bayesian Computation Using Plug-and-Play Priors for Poisson Inverse Problemscited by 2
  8. 2025Plug-and-Play Posterior Sampling for Blind Inverse Problemscited by 2
  9. 2025Solving Inverse Problems using Diffusion with Iterative Colored Renoisingcited by 1
  10. 2025Noise Conditional Variational Score Distillationcited by 1
  11. 2025Diffusion-Prior Split Gibbs Sampling for Synthetic Aperture Radar Imaging under Incomplete Measurementscited by 1
  12. 2026Outlier-robust Diffusion Posterior Sampling for Bayesian Inverse Problemscited by 1
  13. 2026Bayesian Signal Component Decomposition via Diffusion-within-Gibbs Samplingcited by 1
  14. 2026A Gibbs posterior sampler for inverse problem based on prior diffusion modelcited by 1
  15. 2026Optimizing Diffusion Priors in Image Reconstruction from a Single Observationcited by 1
  16. 2026Composing diffusion priors with explicit physical context via generative Gibbs samplingcited by 1
  17. 2026Zeroth-Order Non-Log-Concave Sampling with Variance Reduction and Applications to Inverse Problemscited by 1
  18. 2025LatentINDIGO: An INN-Guided Latent Diffusion Algorithm for Image Restorationcited by 0
  19. 2025Hypothesis Testing in Imaging Inverse Problemscited by 0
  20. 2025Clustering by Denoising: Latent plug-and-play diffusion for single-cell datacited by 0
  21. 2025Bregman geometry-aware split Gibbs sampling for Bayesian Poisson inverse problemscited by 0
  22. 2026Beyond Accuracy: Evaluating Posterior Fidelity of Diffusion Inverse Solverscited by 0
  23. 2026Deep unfolding of MCMC kernels: scalable, modular & explainable GANs for high-dimensional posterior samplingcited by 0
  24. 2026Plug-and-Play Diffusion Meets ADMM: Dual-Variable Coupling for Robust Medical Image Reconstructioncited by 0
  25. 2026Unbiased Diffusion Variational Inversion via Principled Posterior Matchingcited by 0
  26. 2026Bayesian Tensor Decomposition with Diffusion Model Priorcited by 0
  27. 2026Bridging data-driven priors via the score function for posterior sampling -- Comparative review and experimental studycited by 0
  28. 2026FlowSGS: Improving Flow Matching Priors for Inverse Imaging with Stochastic Interpolantscited by 0
  29. 2026Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfoldingcited by 0
  30. 2026DAWIS: Data Assimilation with Windowed Inverse Sampling via Multitask Interpolantscited by 0

Similar, not cited

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  1. 2026Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors
  2. 2025Generative Modeling with Bayesian Sample Inference
  3. 2024Diffusive Gibbs Sampling
  4. 2024Conditional sampling within generative diffusion models
  5. 2024Bayesian computation with generative diffusion models by Multilevel Monte Carlo
  6. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors
  7. 2026Leveraging generative models to assist Monte Carlo sampling
  8. 2025Briding Diffusion Posterior Sampling and Monte Carlo methods: a survey