Decoding and Steering Contact Structure in Trajectory Diffusion

When can contact structure read from a partially denoised trajectory support useful intervention? We study trajectory diffusion in three simulated multi-body systems and separate three quantities that are easily conflated: the error of a probe that reads intermediate states, how concentrated the final outcomes of a state are under repeated stochastic continuation, and the realized utility of acting on the readout. Repeated continuations from the same state show that outcomes concentrate during denoising and that, from the middle of the schedule onward, readout error rather than residual randomness dominates the probe's prediction error. The readout is nevertheless directionally useful: one-shot probe ascent transfers from a distance-based proxy target to an orientation-aware geometric diagnostic in all six fixed models tested, and selected multi-step guidance raises held-out joint target-and-quality success by 12.7–20.1 percentage points in the two three-dimensional systems and by 25–30 points in the two-dimensional system under a scene-consistent quality envelope. The same readout is not usable for selection: probability-gated early rejection establishes no gain in yield per computation, although a sixteen-branch empirical probability of the same event, if it were available at no cost, would. A short invariance argument shows what each use requires. Neither requires calibration, so the probe's overconfidence after optimization is beside the point; guidance needs the probe's gradient to align locally with the true success probability, whereas selection needs its scores to rank states like that probability, and the contact readout ranks poorly. The limitation is ranking, not calibration and not a structural limit of selection. We provide the branching, paired-intervention and held-out policy protocols that separate readout error, outcome concentration and intervention utility, with geometric correspondence, trajectory quality and computation reported explicitly.