DeepBayesFlow: A Bayesian Structured Variational Framework for Generalizable Prostate Segmentation via Expressive Posteriors and SDE-Girsanov Uncertainty Modeling

Abstract: Automatic prostate MRI segmentation faces persistent challenges due to inter-patient anatomical variability, blurred tissue boundaries, and distribution shifts arising from diverse imaging protocols. To address these issues, we propose DeepBayesFlow, a novel Bayesian segmentation framework designed to enhance both robustness and generalization across clinical domains. DeepBayesFlow introduces three key innovations: a learnable NF-Posterior module based on normalizing flows that models complex, data-adaptive latent distributions; a NCVI inference mechanism that removes conjugacy constraints to enable flexible posterior learning in high-dimensional settings; and a SDE-Girsanov module that refines latent representations via time-continuous diffusion and formal measure transformation, injecting temporal coherence and physically grounded uncertainty into the inference process. Together, these components allow DeepBayesFlow to capture domain-invariant structural priors while dynamically adapting to domain-specific variations, achieving accurate and interpretable segmentation across heterogeneous prostate MRI datasets.