Longitudinal Flow Matching for Trajectory Modeling

2025-10-03

AI Summary

Modeling irregular, high-dimensional longitudinal trajectories with sparse temporal sampling remains challenging. Method: This paper proposes Interpolative Multi-Marginal Flow Matching (IMMFM), which constructs a continuous-time flow matching objective via piecewise quadratic interpolation paths—departing from conventional pairwise transformation modeling. IMMFM jointly learns the drift term and a data-driven diffusion coefficient under multi-timepoint consistency constraints, enabling robust continuous stochastic dynamic modeling. Theoretical analysis ensures training stability and supports personalized trajectory generation. Contribution/Results: Evaluated on both synthetic benchmarks and real-world neuroimaging longitudinal datasets, IMMFM achieves significant improvements over state-of-the-art methods in prediction accuracy and downstream task performance (e.g., disease progression modeling and biomarker estimation), demonstrating superior capability in capturing complex, subject-specific temporal dynamics under sparse sampling conditions.

Technology Category

• Machine Learning: Multimodal Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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 extit{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.

Problem

• Modeling sparse high-dimensional sequential trajectories
• Learning continuous dynamics from irregular observations
• Capturing intrinsic stochasticity in longitudinal data

Innovation

• Interpolative Multi-Marginal Flow Matching framework
• Piecewise-quadratic interpolation path for flow matching
• Joint optimization of drift and diffusion coefficients