[2603.28324] LDDMM stochastic interpolants: an application to domain uncertainty quantification in hemodynamics

Statistics > Machine Learning arXiv:2603.28324 (stat) [Submitted on 30 Mar 2026] Title:LDDMM stochastic interpolants: an application to domain uncertainty quantification in hemodynamics Authors:Sarah Katz, Francesco Romor, Jia-Jie Zhu, Alfonso Caiazzo View a PDF of the paper titled LDDMM stochastic interpolants: an application to domain uncertainty quantification in hemodynamics, by Sarah Katz and 3 other authors View PDF HTML (experimental) Abstract:We introduce a novel conditional stochastic interpolant framework for generative modeling of three-dimensional shapes. The method builds on a recent LDDMM-based registration approach to learn the conditional drift between geometries. By leveraging the resulting pull-back and push-forward operators, we extend this formulation beyond standard Cartesian grids to complex shapes and random variables defined on distinct domains. We present an application in the context of cardiovascular simulations, where aortic shapes are generated from an initial cohort of patients. The conditioning variable is a latent geometric representation defined by a set of centerline points and the radii of the corresponding inscribed spheres. This methodology facilitates both data augmentation for three-dimensional biomedical shapes, and the generation of random perturbations of controlled magnitude for a given shape. These capabilities are essential for quantifying the impact of domain uncertainties arising from medical image segmentation on the estimati...