# Guiding Vector Field Generation via Score-based Diffusion Model

arXiv: https://arxiv.org/abs/2604.24487 · HTML: https://mlsanity.com/paper/2604.24487/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 11 of its 23 references that are in the map.
- First posted on arXiv 27 Apr 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 11 of 11)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [SafeDiffuser: Safe Planning with Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.00148/) (2023)
- [An Introduction to Flow Matching and Diffusion Models](https://mlsanity.com/paper/2506.02070/) (2025)
- [LAMARL: LLM-Aided Multi-Agent Reinforcement Learning for Cooperative Policy Generation](https://mlsanity.com/paper/2506.01538/) (2025)
- [Singularity-free Guiding Vector Field for Robot Navigation](https://mlsanity.com/paper/2012.01826/) (2020)
- [Guiding vector fields for the distributed motion coordination of mobile robots](https://mlsanity.com/paper/2209.09478/) (2022)
- [Non-singular Cooperative Guiding Vector Field Under a Homotopy Equivalence Transformation](https://mlsanity.com/paper/2308.06934/) (2023)
- [Spontaneous-Ordering Platoon Control for Multirobot Path Navigation Using Guiding Vector Fields](https://mlsanity.com/paper/2311.00976/) (2023)
- [Inverse Kinematics on Guiding Vector Fields for Robot Path Following](https://mlsanity.com/paper/2502.17313/) (2025)

## Built on by (most cited first, 1 of 1)

- [Recovering Weighted Tangent Geometry from a Single-Scale Score Field](https://mlsanity.com/paper/2608.22334/) (2026)

## Abstract (arXiv)

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.