Measuring and Correcting Prior Transmission in Causal Video Diffusion

A video that follows a requested trajectory may reflect effective control, motion that also appears in an unguided rollout from the same seed, or both. Yet evaluation based on target error alone does not reveal how much the controller improves on unguided generation or whether the remaining error reflects a predictable motion tendency. We introduce TrajectoryBench, a paired evaluation protocol that compares guided and unguided rollouts from matched conditioning and seeds, distinguishing final trajectory adherence from the improvement supplied by control. Across ten seeds on CausVid, controlled displacement is coupled to matched unguided displacement: roughly half of the unguided motion variation survives into the controlled output. We call the slope of this relationship prior transmission. The coupling persists after removing shared directional drift, survives replacement of the evaluation tracker, and appears on a second causal backbone, Causal Forcing. Predictable residual motion is not only an evaluation concern: it is a signal for improving control. We introduce Warp Forcing, a training-free trajectory controller for few-step causal video diffusion that steers objects block by block and adapts its commands to realized motion. Using the protocol's matched unguided rollout as a preview, drift compensation reduces mean path error relative to uncorrected Warp Forcing by 25% on CausVid and 38% on Causal Forcing across three seeds. A preview-free online estimator needs no extra rollout and adds no runtime: on Causal Forcing it matches the matched-preview correction, and on CausVid it recovers about one-third of the preview-based improvement. Measuring matched unguided motion thus yields both more informative evaluation and more accurate trajectory control.