KineFlow: Kinematic Second-Order Flow Matching for Time-Series Forecasting

Conventional time-series discriminative forecasting relies on point-wise regression, which inherently induces over-smoothing and fails to capture stochastic volatility in complex systems. While first-order generative flow matching methods mitigate this issue, they ignore system inertia, resulting in phase-space ambiguities and high sensitivity to noise. We introduce KineFlow, a generative time-series forecasting framework that augments flow matching with a phase-space Neural Acceleration Field, treating exogenous inputs as driving forces that produce gradual momentum shifts rather than abrupt state perturbations. This second-order formulation serves as a structural filter via double integration, suppressing high-frequency noise and producing robust, physically consistent predictions. Extensive experiments on six real-world benchmarks demonstrate that KineFlow achieves an average 15% MSE improvement over discriminative baselines and an 8% gain in CRPS compared to state-of-the-art generative methods.