# Score-Based Turbo Message Passing for Plug-and-Play Compressive Imaging

arXiv: https://arxiv.org/abs/2512.14435 · HTML: https://mlsanity.com/paper/2512.14435/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 30 of its 60 references that are in the map.
- First posted on arXiv 16 Dec 2025.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Regularization by Denoising: Clarifications and New Interpretations](https://mlsanity.com/paper/1806.02296/) (2018)
- [Maximum Likelihood Training for Score-Based Diffusion ODEs by High-Order Denoising Score Matching](https://mlsanity.com/paper/2206.08265/) (2022)
- [An Online Plug-and-Play Algorithm for Regularized Image Reconstruction](https://mlsanity.com/paper/1809.04693/) (2018)
- [From Denoising to Compressed Sensing](https://mlsanity.com/paper/1406.4175/) (2014)
- [AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing](https://mlsanity.com/paper/2004.10078/) (2020)
- [Learned D-AMP: Principled Neural Network based Compressive Image Recovery](https://mlsanity.com/paper/1704.06625/) (2017)
- [Estimating High Order Gradients of the Data Distribution by Denoising](https://mlsanity.com/paper/2111.04726/) (2021)
- [Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems](https://mlsanity.com/paper/2211.12343/) (2022)
- [Regularization by Denoising via Fixed-Point Projection (RED-PRO)](https://mlsanity.com/paper/2008.00226/) (2020)
- [Quantized Compressed Sensing with Score-based Generative Models](https://mlsanity.com/paper/2211.13006/) (2022)
- [QCM-SGM+: Improved Quantized Compressed Sensing With Score-Based Generative Models](https://mlsanity.com/paper/2302.00919/) (2023)
- [Score-Based Turbo Message Passing for Plug-and-Play Compressive Image Recovery](https://mlsanity.com/paper/2503.22140/) (2025)

## Abstract (arXiv)

Message-passing algorithms have been adapted for compressive imaging by incorporating various off-the-shelf image denoisers. However, these denoisers rely largely on generic or hand-crafted priors and often fall short in accurately capturing the complex statistical structure of natural images. As a result, traditional plug-and-play (PnP) methods often lead to suboptimal reconstruction, especially in highly underdetermined regimes. Recently, score-based generative models have emerged as a powerful framework for accurately characterizing sophisticated image distributions. Yet, their direct use for posterior sampling typically incurs prohibitive computational complexity. In this paper, by exploiting the close connection between score-based generative modeling and empirical Bayes denoising, we devise a message-passing framework that integrates a score-based minimum mean-squared error (MMSE) denoiser for compressive image recovery. The resulting algorithm, named score-based turbo message passing (STMP), combines the fast convergence of message passing with the expressive power of score-based generative priors. For practical systems with quantized measurements, we further propose quantized STMP (Q-STMP), which augments STMP with a component-wise MMSE dequantization module. We demonstrate that the asymptotic performance of STMP and Q-STMP can be accurately predicted by a set of state-evolution (SE) equations. Experiments on the FFHQ dataset demonstrate that STMP strikes a significantly better performance-complexity tradeoff compared with competing baselines, and that Q-STMP remains robust even under 1-bit quantization. Remarkably, both STMP and Q-STMP typically converge within 10 iterations.