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
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:3871-3879, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-islam26a, title = { Longitudinal Flow Matching for Trajectory Modeling }, author = {Islam, Mohammad Mohaiminul and Kuipers, Thijs P. and Vadgama, Sharvaree and de Vente, Coen and Khan, Afsana and S{\'a}nchez, Clara I. and Bekkers, Erik J}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {3871--3879}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/islam26a/islam26a.pdf}, url = {https://proceedings.mlr.press/v300/islam26a.html}, 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. } }
Endnote
%0 Conference Paper %T Longitudinal Flow Matching for Trajectory Modeling %A Mohammad Mohaiminul Islam %A Thijs P. Kuipers %A Sharvaree Vadgama %A Coen de Vente %A Afsana Khan %A Clara I. Sánchez %A Erik J Bekkers %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-islam26a %I PMLR %P 3871--3879 %U https://proceedings.mlr.press/v300/islam26a.html %V 300 %X 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.
APA
Islam, M.M., Kuipers, T.P., Vadgama, S., de Vente, C., Khan, A., Sánchez, C.I. & Bekkers, E.J.. (2026). Longitudinal Flow Matching for Trajectory Modeling . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:3871-3879 Available from https://proceedings.mlr.press/v300/islam26a.html.

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