We consider the problem of inferring the behavior of a target system given cues in the form of a time-series taken from another co-evolving system. We show how to approximate the target system's dynamical manifold with a probabilistic model, then compute trajectories on this manifold that are optimal w.r.t. the target system's dynamics and w.r.t. configural clues in the cue signal. The resulting method integrates information over the entire time-series to disambiguate many-to-many mappings between cue configurations and target configurations, yet can run in linear time. We demonstrate with systems that infer 3D nonrigid motion from image cues and, in the case of facial motion, from audio.