用连续动态建模稀疏轨迹，提升预测精度与个体差异捕捉。
Longitudinal Flow Matching for Trajectory Modeling
- 设计分段二次插值路径，联合优化漂移与数据驱动扩散系数。
- 在合成与真实神经影像数据上，预测准确率优于现有方法。
- 适合建模不规则采样、高维、个体差异大的纵向轨迹数据。
序列生成模型常难以处理稀疏采样和高维轨迹，通常将动力学学习简化为成对转移。本文提出插值多边缘流匹配（IMMFM），一种能同时匹配多个观测时间点的连续随机动力学学习框架。IMMFM采用分段二次插值路径作为流匹配的平滑目标，联合优化漂移项与数据驱动的扩散系数，并给出稳定学习的理论条件。该设计能捕捉内在随机性，适应不规则稀疏采样，生成个体特异性轨迹。在合成基准和真实世界纵向神经影像数据集上的实验表明，IMMFM在预测准确率及下游任务表现上均优于现有方法。
原文摘要 · Abstract (English)
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.
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