Generative models for sequential data often struggle with sparsely sampled and high-dimensional trajectories, typically reducing the learning of dynamics to pairwise transitions. We propose Interpolative Multi-Marginal Flow Matching (IMMFM), a framework that learns continuous stochastic dynamics jointly consistent with multiple observed time points. IMMFM employs a piecewise-quadratic interpolation path as a smooth target for flow matching and jointly optimizes drift and a data-driven diffusion coefficient, supported by a theoretical condition for stable learning. This design captures intrinsic stochasticity, handles irregular sparse sampling, and yields subject-specific trajectories. Experiments on synthetic benchmarks and real-world longitudinal neuroimaging datasets show that IMMFM outperforms existing methods in both forecasting accuracy and further downstream tasks.
@article{arxiv.2510.03569,
title = {Longitudinal Flow Matching for Trajectory Modeling},
author = {Mohammad Mohaiminul Islam and Thijs P. Kuipers and Sharvaree Vadgama and Coen de Vente and Afsana Khan and Clara I. Sánchez and Erik J. Bekkers},
journal= {arXiv preprint arXiv:2510.03569},
year = {2025}
}