# Generative Plug and Play: Posterior Sampling for Inverse Problems

arXiv: https://arxiv.org/abs/2306.07233 · HTML: https://mlsanity.com/paper/2306.07233/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 12 Jun 2023.

## Builds on (most cited first, 11 of 11)

- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Score-Based Diffusion Models as Principled Priors for Inverse Imaging](https://mlsanity.com/paper/2304.11751/) (2023)
- [Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation](https://mlsanity.com/paper/1512.07331/) (2015)
- [Plug-and-Play Unplugged: Optimization Free Reconstruction using Consensus Equilibrium](https://mlsanity.com/paper/1705.08983/) (2017)
- [Multi-Slice Fusion for Sparse-View and Limited-Angle 4D CT Reconstruction](https://mlsanity.com/paper/2008.01567/) (2020)

## Built on by (most cited first, 24 of 24)

- [Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction](https://mlsanity.com/paper/2403.17042/) (2024)
- [Provable Probabilistic Imaging using Score-Based Generative Priors](https://mlsanity.com/paper/2310.10835/) (2023)
- [Tutorial on Diffusion Models for Imaging and Vision](https://mlsanity.com/paper/2403.18103/) (2024)
- [An Expectation-Maximization Algorithm for Training Clean Diffusion Models from Corrupted Observations](https://mlsanity.com/paper/2407.01014/) (2024)
- [Plug-and-Play image restoration with Stochastic deNOising REgularization](https://mlsanity.com/paper/2402.01779/) (2024)
- [Plug-and-Play Posterior Sampling under Mismatched Measurement and Prior Models](https://mlsanity.com/paper/2310.03546/) (2023)
- [Strictly Constrained Generative Modeling via Split Augmented Langevin Sampling](https://mlsanity.com/paper/2505.18017/) (2025)
- [Plug-and-Play Priors as a Score-Based Method](https://mlsanity.com/paper/2412.11108/) (2024)
- [Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priors](https://mlsanity.com/paper/2510.10968/) (2025)
- [Learning Cocoercive Conservative Denoisers via Helmholtz Decomposition for Poisson Inverse Problems](https://mlsanity.com/paper/2505.08909/) (2025)
- [PSI3D: Plug-and-Play 3D Stochastic Inference with Slice-wise Latent Diffusion Prior](https://mlsanity.com/paper/2512.18367/) (2025)
- [Stochastic Generative Plug-and-Play Priors](https://mlsanity.com/paper/2604.03603/) (2026)
- [Learning truly monotone operators with applications to nonlinear inverse problems](https://mlsanity.com/paper/2404.00390/) (2024)
- [Plug-and-Play Latent Diffusion for Electromagnetic Inverse Scattering with Application to Brain Imaging](https://mlsanity.com/paper/2509.04860/) (2025)
- [Solving Inverse Problems using Diffusion with Iterative Colored Renoising](https://mlsanity.com/paper/2501.17468/) (2025)
- [Bayesian Signal Component Decomposition via Diffusion-within-Gibbs Sampling](https://mlsanity.com/paper/2602.10792/) (2026)
- [Composing diffusion priors with explicit physical context via generative Gibbs sampling](https://mlsanity.com/paper/2605.10642/) (2026)
- [Zeroth-Order Non-Log-Concave Sampling with Variance Reduction and Applications to Inverse Problems](https://mlsanity.com/paper/2605.30573/) (2026)
- [Supporting renewable energy planning and operation with data-driven high-resolution ensemble weather forecast](https://mlsanity.com/paper/2505.04396/) (2025)
- [Bregman geometry-aware split Gibbs sampling for Bayesian Poisson inverse problems](https://mlsanity.com/paper/2511.12257/) (2025)
- [Diffusion Graph Posterior Sampling for Nonlinear Inverse Problems with Application to Electrical Impedance Tomography](https://mlsanity.com/paper/2605.19621/) (2026)
- [Unbiased Diffusion Variational Inversion via Principled Posterior Matching](https://mlsanity.com/paper/2605.25042/) (2026)
- [Bridging data-driven priors via the score function for posterior sampling -- Comparative review and experimental study](https://mlsanity.com/paper/2606.14800/) (2026)
- [FlowSGS: Improving Flow Matching Priors for Inverse Imaging with Stochastic Interpolants](https://mlsanity.com/paper/2609.20769/) (2026)

## Abstract (arXiv)

Over the past decade, Plug-and-Play (PnP) has become a popular method for reconstructing images using a modular framework consisting of a forward and prior model. The great strength of PnP is that an image denoiser can be used as a prior model while the forward model can be implemented using more traditional physics-based approaches. However, a limitation of PnP is that it reconstructs only a single deterministic image. In this paper, we introduce Generative Plug-and-Play (GPnP), a generalization of PnP to sample from the posterior distribution. As with PnP, GPnP has a modular framework using a physics-based forward model and an image denoising prior model. However, in GPnP these models are extended to become proximal generators, which sample from associated distributions. GPnP applies these proximal generators in alternation to produce samples from the posterior. We present experimental simulations using the well-known BM3D denoiser. Our results demonstrate that the GPnP method is robust, easy to implement, and produces intuitively reasonable samples from the posterior for sparse interpolation and tomographic reconstruction. Code to accompany this paper is available at https://github.com/gbuzzard/generative-pnp-allerton .