Longitudinal Flow Matching for Trajectory Modeling
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909830682247168 |
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| author | Islam, Mohammad Mohaiminul Kuipers, Thijs P. Vadgama, Sharvaree de Vente, Coen Khan, Afsana Sánchez, Clara I. Bekkers, Erik J. |
| author_facet | Islam, Mohammad Mohaiminul Kuipers, Thijs P. Vadgama, Sharvaree de Vente, Coen Khan, Afsana Sánchez, Clara I. Bekkers, Erik J. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_03569 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Longitudinal Flow Matching for Trajectory Modeling Islam, Mohammad Mohaiminul Kuipers, Thijs P. Vadgama, Sharvaree de Vente, Coen Khan, Afsana Sánchez, Clara I. Bekkers, Erik J. Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition 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. |
| title | Longitudinal Flow Matching for Trajectory Modeling |
| topic | Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2510.03569 |