Laminar Flow Matching: Geometric Multiscale Transport for Time-Series Forecasting

Real-world time series exhibit stochastic dynamics across multiple temporal scales, posing a challenge for continuous-time generative forecasting. In standard Flow Matching (FM), a single vector field simultaneously models coarse global evolution and fine-scale fluctuations, which increases transport curvature and leads to inefficient dynamics. We propose Laminar Flow Matching (LFM), a geometry-aware framework that decouples multiscale probability transport into two hierarchically conditioned flows. The Macro-Flow learns a low-curvature global transport path in latent space, while the Micro-Flow models conditionally centered stochastic fluctuations in data space. This hierarchical factorization reduces cross-scale interference and improves transport smoothness and numerical efficiency. Extensive experiments on six real-world datasets show that LFM achieves state-of-the-art performance, reducing MSE by up to 15% and CRPS by 5%, while requiring fewer integration steps than existing generative baselines.