Longitudinal Flow Matching for Trajectory Modeling

• URL: http://arxiv.org/abs/2510.03569v2
• Date: Tue, 07 Oct 2025 23:35:32 GMT
• Title: Longitudinal Flow Matching for Trajectory Modeling
• Authors: Mohammad Mohaiminul Islam, Thijs P. Kuipers, Sharvaree Vadgama, Coen de Vente, Afsana Khan, Clara I. Sánchez, Erik J. Bekkers,
• Abstract summary: We propose Interpolative Multi-Marginal Flow Matching (IMMFM), a framework that learns continuous dynamics jointly consistent with multiple observed time points.<n>IMMFM captures intrinsicity, handles irregular sparse sampling, and yields subject-specific trajectories.<n> Experiments on synthetic benchmarks and real-world longitudinal datasets show that IMMFM outperforms existing methods in both forecasting accuracy and further downstream tasks.
• Score: 7.063657100587108
• License: http://creativecommons.org/licenses/by/4.0/
• 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 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.

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