Guiding Vector Field Generation via Score-based Diffusion Model

2026-04-27

AI Summary

This work addresses the limitations of conventional guiding vector field methods in handling complex trajectories that are unordered, multi-branched, or generated probabilistically. The authors propose the Score-Induced Guiding Vector Field (SGVF) framework, which for the first time integrates score-based diffusion models with guiding vector fields to directly construct vector fields from point cloud data. By incorporating losses enforcing unit norm, orthogonality, and directional consistency, SGVF learns tangent vector fields that accurately capture underlying geometric structures. The method establishes a theoretical connection between vanishing scores in diffusion models and singularities in vector fields, enabling robust handling of intricate geometries such as branching structures and pseudo-manifolds. Experimental results in planar robot navigation demonstrate that SGVF achieves stable and reliable path following in scenarios where traditional approaches fail.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Learning with Manifolds
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Guiding Vector Field
• Path Following
• Unordered Paths
• Multi-branch Paths
• Probabilistic Path Generation

Innovation

• score-based diffusion model
• guiding vector field
• geometric control
• point cloud
• generative modeling