Most prior unsupervised domain adaptation approaches for medical image segmentation are narrowly tailored to either the source-accessible setting, where adaptation is guided by source-target alignment, or the source-free setting, which typically resorts to implicit supervision mechanisms such as pseudo-labeling and model distillation. This substantial divergence in methodological designs between the two settings reveals an inherent flaw: the lack of an explicit, structured construction of anatomical knowledge that naturally generalizes across domains and settings. To bridge this longstanding divide, we introduce a unified, semantically grounded framework that supports both source-accessible and source-free adaptation. Fundamentally distinct from all prior works, our framework's adaptability emerges naturally as a direct consequence of the model architecture, without the need for any handcrafted adaptation strategies. Specifically, our model learns a domain-agnostic probabilistic manifold as a global space of anatomical regularities, mirroring how humans establish visual understanding. Thus, the structural content in each image can be interpreted as a canonical anatomy retrieved from the manifold and a spatial transformation capturing individual-specific geometry. This disentangled, interpretable formulation enables semantically meaningful prediction with intrinsic adaptability. Extensive experiments on challenging cardiac and abdominal datasets show that our framework achieves state-of-the-art results in both settings, with source-free performance closely approaching its source-accessible counterpart, a level of consistency rarely observed in prior works. Beyond quantitative improvement, we demonstrate strong interpretability of the proposed framework via manifold traversal for smooth shape manipulation.
Wang et al. (Tue,) studied this question.