Guiding Vector Field Generation via Score-based Diffusion Model

arXiv cs.RO / 4/28/2026

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Key Points

Guiding Vector Fields (GVFs) are effective for robotic path following, but classical approaches break down for unordered, multi-branch paths and probabilistically generated trajectories.
The paper introduces SGVF (Score-Induced Guiding Vector Field), a unified framework that uses score-based generative modeling to learn guidance vector fields directly from data distributions.
SGVF trains tangent vector fields from point clouds using unit-norm, orthogonality, and directional-consistency losses to preserve geometric fidelity while maintaining control feasibility.
The authors connect diffusion-model score behavior to GVF singularities and show improved representational ability near sharp path curvatures.
Experiments on planar robotic navigation indicate SGVF reliably follows complex topologies (e.g., branching/pseudo-manifolds) where classical GVFs fail, and the project provides code and videos.

Abstract

Guiding Vector Fields (GVFs) are a powerful tool for robotic path following. However, classical methods assume smooth, ordered curves and fail when paths are unordered, multi-branch, or generated by probabilistic models. We propose a unified framework, termed the Score-Induced Guiding Vector Field (SGVF), which leverages score-based generative modeling to construct vector fields directly from data distributions. SGVF learns tangent fields from point clouds with unit-norm, orthogonality, and directional-consistency losses, ensuring geometric fidelity and control feasibility. This approach removes the reliance on ad-hoc path segmentation and enables guidance along complex topologies such as branching and pseudo-manifolds. The study establishes a correspondence between score vanishing in diffusion models and GVF singularities and highlights representational capacity near sharp path curvatures. Experiments on robotic navigation in planar environments demonstrate that SGVF achieves reliable path following in scenarios where classical GVFs fail, underscoring its potential as a bridge between generative modeling and geometric control. Code and experiment video are available at https://github.com/czr-gif/Guiding-Vector-Field-Generation-via-Score-based-Diffusion-Model.