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

arXiv stat.ML / 3/31/2026

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Key Points

The paper proposes a conditional stochastic interpolant framework for generative modeling of 3D shapes using an LDDMM-based registration approach to learn conditional drift between geometries.
It extends the framework to handle complex, non-Cartesian domains by using pull-back and push-forward operators, enabling stochastic interpolation over shapes and random variables defined on distinct domains.
The authors apply the method to cardiovascular/hemodynamics simulations by generating 3D aortic shapes from an initial patient cohort, conditioned on latent geometric parameters (centerline points and sphere radii).
The framework supports both data augmentation and controlled-magnitude random perturbations of a given shape, targeting domain uncertainty quantification.
The main goal is to quantify how medical image segmentation uncertainties propagate to downstream biomedical estimates, such as hemodynamic biomarkers.

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 estimation of relevant biomarkers.