Flow matching is a scalable generative framework for characterizing continuous normalizing flows with wide-range applications. However, current state-of-the-art methods are not well-suited for modeling dynamical systems, as they construct conditional paths using linear interpolants that may not capture the underlying state evolution, especially when learning higher-order dynamics from irregular sampled observations. Constructing unified paths that satisfy multi-marginal constraints across observations is challenging, since naïve higher-order polynomials tend to be unstable and oscillatory. We introduce SplineFlow, a theoretically grounded flow matching algorithm that jointly models conditional paths across observations via B-spline interpolation. Specifically, SplineFlow exploits the smoothness and stability of B-spline bases to learn the complex underlying dynamics in a structured manner while ensuring the multi-marginal requirements are met. Comprehensive experiments across various deterministic and stochastic dynamical systems of varying complexity, as well as on cellular trajectory inference tasks, demonstrate the strong improvement of SplineFlow over existing baselines. Our code is available at: https://github.com/santanurathod/SplineFlow.

翻译：流匹配是一种可扩展的生成框架，用于刻画连续归一化流，具有广泛的应用前景。然而，当前最先进的方法并不适合对动态系统进行建模，因为它们使用线性插值构造条件路径，可能无法捕捉潜在的状态演化过程，尤其是在从非均匀采样观测中学习高阶动态时。构建满足观测间多边际约束的统一路径具有挑战性，因为简单的高阶多项式往往不稳定且易振荡。本文提出SplineFlow，一种基于理论基础的流匹配算法，通过B样条插值联合建模观测间的条件路径。具体而言，SplineFlow利用B样条基函数的平滑性与稳定性，以结构化方式学习复杂的潜在动态，同时确保满足多边际约束条件。在不同复杂度的多种确定性与随机动态系统以及细胞轨迹推断任务上的综合实验表明，SplineFlow相比现有基线方法具有显著的性能提升。我们的代码公开于：https://github.com/santanurathod/SplineFlow。