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

arXiv: https://arxiv.org/abs/2503.22140 · HTML: https://mlsanity.com/paper/2503.22140/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 17 of its 39 references that are in the map.
- First posted on arXiv 28 Mar 2025.

## Placed in

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

## Builds on (most cited first, 17 of 17)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Maximum Likelihood Training for Score-Based Diffusion ODEs by High-Order Denoising Score Matching](https://mlsanity.com/paper/2206.08265/) (2022)
- [From Denoising to Compressed Sensing](https://mlsanity.com/paper/1406.4175/) (2014)
- [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)
- [User-defined Event Sampling and Uncertainty Quantification in Diffusion Models for Physical Dynamical Systems](https://mlsanity.com/paper/2306.07526/) (2023)

## Built on by (most cited first, 2 of 2)

- [Score-Based Turbo Message Passing for Plug-and-Play Compressive Imaging](https://mlsanity.com/paper/2512.14435/) (2025)
- [Diffusion-OAMP for Joint Image Compression and Wireless Transmission](https://mlsanity.com/paper/2604.27952/) (2026)

## Abstract (arXiv)

Message passing algorithms have been tailored for compressive imaging applications by plugging in different types of off-the-shelf image denoisers. These off-the-shelf denoisers mostly rely on some generic or hand-crafted priors for denoising. Due to their insufficient accuracy in capturing the true image prior, these methods often fail to produce satisfactory results, especially in highly underdetermined scenarios. On the other hand, score-based generative modeling offers a promising way to accurately characterize the sophisticated image distribution. In this paper, by exploiting the close relation between score-based modeling and empirical Bayes-optimal denoising, we devise a message passing framework that integrates a score-based minimum mean squared error (MMSE) denoiser for compressive image recovery. Experiments on the FFHQ dataset demonstrate that our method strikes a significantly better performance-complexity tradeoff than conventional message passing, regularized linear regression, and score-based posterior sampling baselines. Remarkably, our method typically converges in fewer than 20 neural function evaluations (NFEs).