{"ID":2861199,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.03569","arxiv_id":"2510.03569","title":"Longitudinal Flow Matching for Trajectory Modeling","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.","short_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...","url_abs":"https://arxiv.org/abs/2510.03569","url_pdf":"https://arxiv.org/pdf/2510.03569v2","authors":"[\"Mohammad Mohaiminul Islam\",\"Thijs P. Kuipers\",\"Sharvaree Vadgama\",\"Coen de Vente\",\"Afsana Khan\",\"Clara I. Sánchez\",\"Erik J. Bekkers\"]","published":"2025-10-03T23:33:50Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"cs.CV\",\"stat.ML\"]","methods":"[\"Diffusion Model\"]","has_code":false}