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

arXiv: https://arxiv.org/abs/2508.12166 · HTML: https://mlsanity.com/paper/2508.12166/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 56 of its 115 references that are in the map.
- First posted on arXiv 16 Aug 2025.

## Builds on (most cited first, 30 of 56)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Solving Rubik's Cube with a Robot Hand](https://mlsanity.com/paper/1910.07113/) (2019)
- [End-to-end Driving via Conditional Imitation Learning](https://mlsanity.com/paper/1710.02410/) (2017)
- [Safe Reinforcement Learning via Shielding](https://mlsanity.com/paper/1708.08611/) (2017)
- [Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age](https://mlsanity.com/paper/1606.05830/) (2016)
- [Learning to Explore using Active Neural SLAM](https://mlsanity.com/paper/2004.05155/) (2020)
- [DESIRE: Distant Future Prediction in Dynamic Scenes with Interacting Agents](https://mlsanity.com/paper/1704.04394/) (2017)
- [LIO-SAM: Tightly-coupled Lidar Inertial Odometry via Smoothing and Mapping](https://mlsanity.com/paper/2007.00258/) (2020)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [Kimera: from SLAM to Spatial Perception with 3D Dynamic Scene Graphs](https://mlsanity.com/paper/2101.06894/) (2021)
- [DESPOT: Online POMDP Planning with Regularization](https://mlsanity.com/paper/1609.03250/) (2016)
- [An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization](https://mlsanity.com/paper/2404.07771/) (2024)
- [DiffTraj: Generating GPS Trajectory with Diffusion Probabilistic Model](https://mlsanity.com/paper/2304.11582/) (2023)
- [STRAP: Robot Sub-Trajectory Retrieval for Augmented Policy Learning](https://mlsanity.com/paper/2412.15182/) (2024)
- [DiffuserLite: Towards Real-time Diffusion Planning](https://mlsanity.com/paper/2401.15443/) (2024)
- [Potential Based Diffusion Motion Planning](https://mlsanity.com/paper/2407.06169/) (2024)
- [Multi-Robot Motion Planning with Diffusion Models](https://mlsanity.com/paper/2410.03072/) (2024)
- [Differentiable SLAM-net: Learning Particle SLAM for Visual Navigation](https://mlsanity.com/paper/2105.07593/) (2021)
- [Deep Reinforcement Learning for Wireless Sensor Scheduling in Cyber-Physical Systems](https://mlsanity.com/paper/1809.05149/) (2018)
- [Particle Filter SLAM for Vehicle Localization](https://mlsanity.com/paper/2402.07429/) (2024)
- [HyP-DESPOT: A Hybrid Parallel Algorithm for Online Planning under Uncertainty](https://mlsanity.com/paper/1802.06215/) (2018)
- [DDAT: Diffusion Policies Enforcing Dynamically Admissible Robot Trajectories](https://mlsanity.com/paper/2502.15043/) (2025)
- [EcoFusion: Energy-Aware Adaptive Sensor Fusion for Efficient Autonomous Vehicle Perception](https://mlsanity.com/paper/2202.11330/) (2022)
- [Resisting Stochastic Risks in Diffusion Planners with the Trajectory Aggregation Tree](https://mlsanity.com/paper/2405.17879/) (2024)
- [Motion Primitives-based Navigation Planning using Deep Collision Prediction](https://mlsanity.com/paper/2201.03254/) (2022)

## Built on by (most cited first, 1 of 1)

- [Muninn: Your Trajectory Diffusion Model But Faster](https://mlsanity.com/paper/2605.09999/) (2026)

## Abstract (arXiv)

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 textitminimal sensor subset must be active at each location to maintain state uncertainty textitjust 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.