arXiv:2610.27869v1 Announce Type: new Abstract: We consider the following inverse domain uncertainty quantification problem: given a prescribed value or measurement of a hemodynamic biomarker, characterize the distribution of vascular geometries compatible with it. The problem is formulated as a Bayesian inverse problem in which a high-dimensional latent parameter encodes the cardiovascular shape and accounts for inter-patient variability. The parameter-to-observable map composes a conditional LDDMM stochastic interpolant generating the aortic surface with a high-performance numerical finite element solver for the unsteady incompressible Navier--Stokes equations, from which biomarkers of interest are evaluated. The map is nonlinear, high-dimensional and computationally expensive. To address the problem, we compare three ensemble strategies: ensemble adjusted Kalman inversion (EAKI), adaptive Bayesian updating with structural reliability (aBUS), and a Wasserstein--Fisher--Rao (WFR) sequential Monte Carlo scheme. The first two approaches are derivative-free. For the third method, we introduce a novel differentiable flow-matching surrogate that reduces the cost of a single forward map evaluation at the price of a distribution shift depending on the training distribution used for the surrogate. We apply the framework to the generation of virtual patient cohorts matching prescribed pressure drops along aortic geometries affected by coarctation, and we validate and compare the three methods on synthetic data.