Deep Computational Anatomy via Latent-Aligned Multiview Normalizing Flows

In modeling complex probability distributions, normalizing flows provide exact-likelihood, bijective mappings between empirical data and tractable latent spaces. Building on this foundation, latent-aligned multiview normalizing (LAMNr) flows leverage these salient properties to learn shared latent subspaces across heterogeneous, multimodal datasets while simultaneously topologically unfolding the sampled data manifold into a continuous vector space. Formal latent-alignment constraints are used to model shared structural features separate from view-specific variations, coordinating latent projections into a shared geometric subspace. By applying this transformation in the context of biological imaging, the framework establishes a potential basis for a deep learning interpretation of foundational computational anatomy concepts, such as the population template, latent distances, and geodesic pairwise image interpolation. Additionally, the proposed framework enables closed-form conditional modeling for exact cross-view imputation and other latent space manipulations. Evaluations and illustrations on both imaging-derived phenotypes (IDPs) and multimodal MRI demonstrate the proposed framework and potential applications. To further motivate our work, we provide a robust and comprehensive, 2D and 3D open-source implementation in PyTorch, natively integrated with the ANTsX ecosystem (i.e., ANTsTorch) for efficient training and subsequent data transformation, manipulation, and analysis.