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

Zhuoyi Fang

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.

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.

Paper Structure

This paper contains 16 sections, 11 equations, 2 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. Deep learning for prostate image segmentation
  4. Domain generalization for medical image segmentation
  5. Method
  6. Model Overall
  7. Normalizing Flow for Posterior Modeling of Latent Variable $z$
  8. Non-Conjugate Variational Inference for Flexible Posterior Learning
  9. Advanced SDE-based Latent Diffusion with Girsanov Transformation
  10. Spatial Priors, Discrete Segmentation, and Bayesian Regularization
  11. Experiments
  12. Datasets
  13. Implementation Details
  14. Results
  15. Discussion
  16. ...and 1 more sections

Figures (2)

  • Figure 1: Model Architecture Overview of DeepBayesFlow.
  • Figure 2: The visualization results of the proposed DeepBayesFlow model against other state-of-the-arts.