Residual Jump Flow Matching for Extreme-Event Time-Series Generation

In linear flow matching, the large increments that define time-series extremes share one transport target with background variation and can be underrepresented by a finite velocity model. We introduce Residual Jump Flow Matching (RJFM), centered on a cumulative-residual probability path that separates large increments from a base trajectory and transports their persistent effect later in generative time. The path preserves both endpoints while changing the regression geometry; we quantify its maximum displacement from linear interpolation and its additional kinetic action. A structured temporal velocity with base and cumulative-increment branches provides an architectural refinement of this path design. Across nine real time series, RJFM improves tail and extreme-increment fidelity over capacity-matched flow baselines and diffusion models.