# Training-Free Diffusion Planning with Analytical Local Scores

arXiv: https://arxiv.org/abs/2610.01959 · HTML: https://mlsanity.com/paper/2610.01959/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 24 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 14 of 14)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [Global Convergence of Langevin Dynamics Based Algorithms for Nonconvex Optimization](https://mlsanity.com/paper/1707.06618/) (2017)
- [Constrained Synthesis with Projected Diffusion Models](https://mlsanity.com/paper/2402.03559/) (2024)
- [Searching with Consistent Prioritization for Multi-Agent Path Finding](https://mlsanity.com/paper/1812.06356/) (2018)
- [Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference](https://mlsanity.com/paper/1707.07383/) (2017)
- [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)
- [Simultaneous Multi-Robot Motion Planning with Projected Diffusion Models](https://mlsanity.com/paper/2502.03607/) (2025)
- [CoBL-Diffusion: Diffusion-Based Conditional Robot Planning in Dynamic Environments Using Control Barrier and Lyapunov Functions](https://mlsanity.com/paper/2406.05309/) (2024)
- [Full-Order Sampling-Based MPC for Torque-Level Locomotion Control via Diffusion-Style Annealing](https://mlsanity.com/paper/2409.15610/) (2024)
- [Discrete-Guided Diffusion for Scalable and Safe Multi-Robot Motion Planning](https://mlsanity.com/paper/2508.20095/) (2025)
- [Efficient Multi-Agent Trajectory Planning with Feasibility Guarantee using Relative Bernstein Polynomial](https://mlsanity.com/paper/1909.10219/) (2019)
- [Simulation-Informed Diffusion for Decentralized Multi-robot Motion Planning](https://mlsanity.com/paper/2605.27697/) (2026)

## Abstract (arXiv)

Path finding and multi-robot motion planning require trajectories that are smooth, goal-directed, and collision-free in environments with complex geometric constraints. Recent diffusion-based planners have shown that trajectory generation can be cast as iterative denoising which has opened the doors to learning-based approaches that can handle multi-modal trajectory distributions and refine entire trajectories. However, a key limitation is that diffusion planners require training on large collections of feasible trajectories, rendering them map-specific, and difficult to deploy when high-quality demonstrations are unavailable. This paper introduces a training-free diffusion-based motion planner that replaces learned global trajectory scores with analytical local scores derived from obstacle, smoothness, velocity, and inter-agent feasibility terms. The proposed idea relies on a key observation: the score of a trajectory can be reconstructed by considering only local interactions between neighboring waypoints and nearby constraints. This structure exploitation yields a decomposed denoising procedure that retains the optimization structure of classical trajectory methods while inheriting the iterative refinement behavior of diffusion models. Experiments on a large collection of complex environments and large multi-agent planning tasks show that the proposed analytical score produces smooth and feasible trajectories within limited computational costs, for example in generating feasible paths for 300+ agents in environments containing 100+ obstacles in under 6 seconds on a GPU, outperforming strong learning-based and optimization baselines, while avoiding the data requirements of learned diffusion planners.