# Plug-and-Play Latent Diffusion for Electromagnetic Inverse Scattering with Application to Brain Imaging

arXiv: https://arxiv.org/abs/2509.04860 · HTML: https://mlsanity.com/paper/2509.04860/

## 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 28 of its 77 references that are in the map.
- First posted on arXiv 5 Sep 2025.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Variational Autoencoder for Deep Learning of Images, Labels and Captions](https://mlsanity.com/paper/1609.08976/) (2016)
- [Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors](https://mlsanity.com/paper/2405.18782/) (2024)
- [Diffusion Models in Low-Level Vision: A Survey](https://mlsanity.com/paper/2406.11138/) (2024)
- [Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction](https://mlsanity.com/paper/2403.17042/) (2024)
- [Diffusion Models, Image Super-Resolution And Everything: A Survey](https://mlsanity.com/paper/2401.00736/) (2024)
- [Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization](https://mlsanity.com/paper/2205.02640/) (2022)
- [DeepNIS: Deep Neural Network for Nonlinear Electromagnetic Inverse Scattering](https://mlsanity.com/paper/1810.03990/) (2018)
- [Generative Plug and Play: Posterior Sampling for Inverse Problems](https://mlsanity.com/paper/2306.07233/) (2023)
- [Physics Embedded Machine Learning for Electromagnetic Data Imaging](https://mlsanity.com/paper/2207.12607/) (2022)
- [Deep Injective Prior for Inverse Scattering](https://mlsanity.com/paper/2301.03092/) (2023)
- [Real-Time Model-Based Quantitative Ultrasound and Radar](https://mlsanity.com/paper/2402.10520/) (2024)
- [ADMM-based multi-parameter wavefield reconstruction inversion in VTI acoustic media with TV regularization](https://mlsanity.com/paper/1905.05452/) (2019)
- [A Physics-Driven AI Approach for Microwave Imaging of Breast Tumors](https://mlsanity.com/paper/2401.02715/) (2024)

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

- [A Model-Guided Neural Network Method for the Inverse Scattering Problem](https://mlsanity.com/paper/2512.10123/) (2025)
- [Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding](https://mlsanity.com/paper/2609.30539/) (2026)

## Abstract (arXiv)

Electromagnetic (EM) imaging is an important tool for non-invasive sensing with low-cost and portable devices. One emerging application is EM stroke imaging, which enables early diagnosis and continuous monitoring of brain strokes. Quantitative imaging is achieved by solving an inverse scattering problem (ISP) that reconstructs permittivity and conductivity maps from measurements. In general, the reconstruction accuracy is limited by its inherent nonlinearity and ill-posedness. Existing methods, including learning-free and learning-based approaches, fail to either incorporate complicated prior distributions or provide theoretical guarantees, posing difficulties in balancing interpretability, distortion error, and reliability. To overcome these limitations, we propose a posterior sampling method based on latent diffusion for quantitative EM brain imaging, adapted from a generative plug-and-play (PnP) posterior sampling framework. Our approach allows to flexibly integrate prior knowledge into physics-based inversion without requiring paired measurement-label datasets. We first learn the prior distribution of targets from an unlabeled dataset, and then incorporate the learned prior into posterior sampling. In particular, we train a latent diffusion model on permittivity and conductivity maps to capture their prior distribution. Then, given measurements and the forward model describing EM wave physics, we perform posterior sampling by alternating between two samplers that respectively enforce the likelihood and prior distributions. Finally, reliable reconstruction is obtained through minimum mean squared error (MMSE) estimation based on the samples. Experimental results on brain imaging demonstrate that our approach achieves state-of-the-art performance in reconstruction accuracy and structural similarity while maintaining high measurement fidelity.