Longitudinal Flow Matching for Trajectory Modeling
This addresses challenges in trajectory modeling for domains like neuroimaging, though it appears incremental as it builds on flow matching methods.
The paper tackles the problem of generative modeling for sparsely sampled and high-dimensional trajectories by proposing Interpolative Multi-Marginal Flow Matching (IMMFM), which learns continuous stochastic dynamics consistent with multiple time points, resulting in improved forecasting accuracy and downstream task performance on synthetic and real-world neuroimaging datasets.
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.