Trajectory Replay In Sequential Flow Matching: Concentration and Coverage

Recent work on sequential flow matching shows that the infinite-capacity empirical velocity field is a kernel regressor over stored transitions, approaching nearest-neighbour trajectory replay as its weights concentrate. We characterise when this occurs and identify which modelling choices control it. For Gaussian conditional paths, we characterise the onset of replay, its behaviour in high dimensions, and how it depends on the geometry of the stored transitions and the choice of conditional path. We further show that, under constant-in-flow-time covariance, the empirical field remains within the convex hull of the stored velocity targets, imposing a representation floor that cannot be overcome by reweighting. Experiments on chaotic systems validate the predicted concentration and coverage behaviour, while finite-capacity experiments show that neural networks can depart from the empirical minimiser and thereby mitigate replay. Together, these results distinguish replay concentration from target coverage, showing that controlling replay alone does not guarantee accurate prediction.