Projection-Dominated Inference-Time Scaling in Diffusion Planning

Sampling a plan from a trajectory diffusion model is now a standard way to spend inference-time compute on control, but "more compute helps" hides which error it helps. This paper shows that the achieved regret of a diffusion planner, the suboptimality of the executable plan, splits exactly into a feasibility term (the cost of making the sample executable) and a relaxed-optimisation term. On a planar-quadrotor testbed the second term does not fall with any inference-compute knob for a goal-conditioned planner, and the first dominates, since a sub-5% per-step dynamics defect becomes a metres-scale endpoint error over the horizon. Denoising steps and best-of-N barely reduce the feasibility term, because the sampled defect is at a score-error floor by two steps, an expressivity limit of the model class. Nearest-point projection iterations K drive it down as $K^{-1}$, a rate that follows from the rollout-to-controls Jacobian having effective rank below 2 out of 128, and that a 100x better conditioned linear double integrator loses. The budget rule, a few denoising steps and the rest into projection, is verified against a grid.