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

2026-03-31

AI Summary

Existing diffusion-based trajectory planning methods rely heavily on large-scale training data or known dynamics models, limiting their applicability in model-free, training-free settings. This work proposes a novel trajectory planning approach that requires neither training nor explicit dynamics models, introducing the first “training- and model-free” diffusion planning framework. It achieves multi-scale nonparametric regression through a tripartite kernel mechanism—encompassing diffusion proximity, state context, and goal relevance—and directly computes the diffusion score function from a small trajectory library using Nadaraya-Watson kernel estimation. Safety is ensured via noise scheduling and mask-based rollback strategies. Evaluated on four robotic systems using only 1,000 pre-collected trajectories, the method attains 98.5% of the average return achieved by model-based baselines and substantially outperforms nearest-neighbor retrieval by 18%–63%.

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.

Problem

• diffusion-based trajectory optimization
• score estimation
• model-free planning
• trajectory data
• nonparametric regression

Innovation

• score diffusion
• model-free planning
• kernel-based estimation
• nonparametric regression
• trajectory optimization