Behavioral Score Diffusion: Model-Free Trajectory Planning via Kernel-Based Score Estimation from Data

TL;DR

Behavioral Score Diffusion (BSD) is a novel, training-free trajectory planning method that estimates diffusion scores directly from data using kernel methods, enabling effective model-free planning in complex robotic systems.

Contribution

BSD introduces a kernel-based, training-free diffusion score estimation approach for trajectory planning, eliminating the need for learned models or analytical dynamics.

Findings

BSD achieves 98.5% of model-based reward with only 1,000 trajectories.

BSD outperforms nearest-neighbor retrieval by 18-63%.

BSD effectively handles nonlinear dynamics without linearization.

Abstract

Diffusion-based trajectory optimization has emerged as a powerful planning paradigm, but existing methods require either learned score networks trained on large datasets or analytical dynamics models for score computation. We introduce \emph{Behavioral Score Diffusion} (BSD), a training-free and model-free trajectory planner that computes the diffusion score function directly from a library of trajectory data via kernel-weighted estimation. At each denoising step, BSD retrieves relevant trajectories using a triple-kernel weighting scheme -- diffusion proximity, state context, and goal relevance -- and computes a Nadaraya-Watson estimate of the denoised trajectory. The diffusion noise schedule naturally controls kernel bandwidths, creating a multi-scale nonparametric regression: broad averaging of global behavioral patterns at high noise, fine-grained local interpolation at low noise. This coarse-to-fine structure handles nonlinear dynamics without linearization or parametric assumptions. Safety is preserved by applying shielded rollout on kernel-estimated state trajectories, identical to existing model-based approaches. We evaluate BSD on four robotic systems of increasing complexity (3D--6D state spaces) in a parking scenario. BSD with fixed bandwidth achieves 98.5\% of the model-based baseline's average reward across systems while requiring no dynamics model, using only 1{,}000 pre-collected trajectories. BSD substantially outperforms nearest-neighbor retrieval (18--63\% improvement), confirming that the diffusion denoising mechanism is essential for effective data-driven planning.