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.