Along with conditional flow matching and rectifying flows, stochastic interpolants have emerged as a versatile framework for generative modelling. While these methodologies demonstrate exceptional performance in applications involving images or snapshots on Cartesian grids, their extension to more complex domains, such as shapes or surfaces, poses significant challenges. Furthermore, the implementation of mini-batch optimal transport for kinetic energy density minimisation, while relatively straightforward on Cartesian grids, becomes computationally prohibitive and less practical when applied to general three-dimensional meshes with varying geometries. To address these limitations, we propose a novel approach based on graph neural networks and Large Deformation Diffeomorphic Metric Mapping (LDDMM) for conditional flow matching, building upon prior work. We present applications in the context of time-dependent cardiovascular simulations and shape-informed reduced-order modelling. This methodology facilitates data augmentation for three-dimensional biomedical shapes and also enables the generation of random perturbations of prescribed magnitudes for given shapes. Such capabilities are pivotal for quantifying the impact of uncertainties in the definition of computational domains from medical images on the estimation of relevant biomarkers. Inter-patient surrogate modelling for time-dependent cardiovascular simulations is also demonstrated through autoregressive conditional stochastic interpolants.