Longitudinal Flow Matching for Trajectory Modeling

Mohammad Mohaiminul Islam, Thijs P. Kuipers, Sharvaree Vadgama, Coen de Vente, Afsana Khan, Clara I. Sánchez, Erik J Bekkers

Abstract: 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 \textit{Interpolative Multi-Marginal Flow Matching} (IMMFM), a framework that learns continuous stochastic dynamics jointly consistent with multiple observed time points. IMMFM employs a 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.

Code Dataset Promise: No

Code Dataset Url: https://github.com/niazoys/longitudinal-flow-matching

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Submission Number: 1678