Guiding Vector Field Generation Via Score-Based Diffusion Model
Zirui Chen, shiliang guo, Shiyu Zhao
AI summary
Problem
Classical guiding vector fields rely on smooth, ordered, and parameterized curves, making them ineffective for modern data-driven paths that are unordered, multi-branch, or generated by probabilistic models.
Approach
The authors introduce SGVF, which learns a gradient score field from raw point clouds using diffusion models and combines it with a learned orthogonal tangent field to construct a unified guiding vector field without explicit path parameterization.
Key results
- Unified framework for following unordered, branching, and probabilistic paths
- Direct inference of manifold geometry from raw point clouds via learned score fields
- Theoretical correspondence between score vanishing and GVF singularities
- Demonstrated reliable path following in planar robotic navigation where classical methods fail
Why it matters
Enables robots to navigate complex, data-driven paths without manual segmentation, bridging generative AI and geometric control.
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, orthog- onality, and directional-consistency losses, ensuring geometric fidelity and control feasibility. This approach removes the re- liance 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 repre- sentational capacity near sharp path curvatures. Experiments on robotic navigation in planar environments demonstrate that SGVF achieves reliable path following in scenarios where clas- sical GVFs fail, underscoring its potential as a bridge between generative modeling and geometric control. Code and experi- ment video are available at https://github.com/czr-gif/Guiding- Vector-Field-Generation-via-Score-based-Diffusion-Model.