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

arXiv: https://arxiv.org/abs/2603.28324 · HTML: https://mlsanity.com/paper/2603.28324/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 54 references that are in the map.
- First posted on arXiv 30 Mar 2026.

## Builds on (most cited first, 18 of 18)

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- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Sora: A Review on Background, Technology, Limitations, and Opportunities of Large Vision Models](https://mlsanity.com/paper/2402.17177/) (2024)
- [Uncertain-DeepSSM: From Images to Probabilistic Shape Models](https://mlsanity.com/paper/2007.06516/) (2020)
- [GenPhys: From Physical Processes to Generative Models](https://mlsanity.com/paper/2304.02637/) (2023)
- [Flow Matching Meets Biology and Life Science: A Survey](https://mlsanity.com/paper/2507.17731/) (2025)
- [ResNet-LDDMM: Advancing the LDDMM Framework using Deep Residual Networks](https://mlsanity.com/paper/2102.07951/) (2021)
- [Physics-aware generative models for turbulent fluid flows through energy-consistent stochastic interpolants](https://mlsanity.com/paper/2504.05852/) (2025)
- [Telegrapher's Generative Model via Kac Flows](https://mlsanity.com/paper/2506.20641/) (2025)
- [Geometric Uncertainty in Patient-Specific Cardiovascular Modeling with Convolutional Dropout Networks](https://mlsanity.com/paper/2009.07395/) (2020)
- [Deformable registration and generative modelling of aortic anatomies by auto-decoders and neural ODEs](https://mlsanity.com/paper/2506.00947/) (2025)
- [Geometric Uncertainty of Patient-Specific Blood Vessels and its Impact on Aortic Hemodynamics](https://mlsanity.com/paper/2410.19472/) (2024)
- [Graph-Convolutional-Beta-VAE for Synthetic Abdominal Aorta Aneurysm Generation](https://mlsanity.com/paper/2506.13628/) (2025)
- [Impact of Turbulence Modeling on the Simulation of Blood Flow in Aortic Coarctation](https://mlsanity.com/paper/2208.14217/) (2022)

## Abstract (arXiv)

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.