Belief-Conditioned One-Step Diffusion: Real-Time Trajectory Planning with Just-Enough Sensing

Abstract: Robots equipped with rich sensor suites can localize reliably in partially-observable environments, but powering every sensor continuously is wasteful and often infeasible. Belief-space planners address this by propagating pose-belief covariance through analytic models and switching sensors heuristically--a brittle, runtime-expensive approach. Data-driven approaches--including diffusion models--learn multi-modal trajectories from demonstrations, but presuppose an accurate, always-on state estimate. We address the largely open problem: for a given task in a mapped environment, which \textit{minimal sensor subset} must be active at each location to maintain state uncertainty \textit{just low enough} to complete the task? Our key insight is that when a diffusion planner is explicitly conditioned on a pose-belief raster and a sensor mask, the spread of its denoising trajectories yields a calibrated, differentiable proxy for the expected localisation error. Building on this insight, we present Belief-Conditioned One-Step Diffusion (B-COD), the first planner that, in a 10 ms forward pass, returns a short-horizon trajectory, per-waypoint aleatoric variances, and a proxy for localisation error--eliminating external covariance rollouts. We show that this single proxy suffices for a soft-actor-critic to choose sensors online, optimising energy while bounding pose-covariance growth. We deploy B-COD in real-time marine trials on an unmanned surface vehicle and show that it reduces sensing energy consumption while matching the goal-reach performance of an always-on baseline.