Dual-VaDE: Efficient and Robust Prototype Learning via Variational Dual-Domain Mixture Priors

Abstract

In this paper, we propose Dual-VaDE, an unsupervised generative framework for learning interpretable anatomical prototypes from unlabeled medical images. In contrast to previous variational methods that rely on a single spatial latent code, which often entangles global geometry with local textures and fails to capture their cross-domain dependencies, Dual-VaDE introduces a dual-domain Gaussian mixture prior that explicitly couples spatial anatomy with phase-preserving Fourier spectral representations. We derive an exact, closed-form variational lower bound that fuses this joint prior into the decoder and optimizes the entire network end-to-end via an alternating EM formulation, avoiding heuristic two-stage clustering while ensuring superior training stability and robustness. Evaluated on OASIS-3 brain MRI, Dual-VaDE delivers substantially sharper and more plausible prototypes, achieves superior cluster separation with improvements of up to 94% over spatial-only baselines, exhibits markedly reduced variance across random seeds, and incurs negligible inference overhead (0.28 ms per image).