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.

翻译：引导向量场是机器人路径跟踪的强大工具。然而，经典方法假设路径光滑有序，当路径无序、存在多分支或由概率模型生成时则会失效。我们提出一个统一框架——称为分数诱导引导向量场，该框架利用基于分数的生成式建模直接从数据分布构建向量场。SGVF通过单位范数、正交性和方向一致性损失从点云中学习切向量场，从而确保几何保真度和控制可行性。该方法消除了对临时路径分割的依赖，并能在分支和伪流形等复杂拓扑结构上实现引导。本研究建立了扩散模型中分数消失与GVF奇异性之间的对应关系，并突出了在路径急剧曲率附近的表示能力。在平面环境中进行的机器人导航实验表明，SGVF在经典GVF失效的场景中实现了可靠的路径跟踪，突显了其作为生成式建模与几何控制之间桥梁的潜力。代码和实验视频可在https://github.com/czr-gif/Guiding-Vector-Field-Generation-via-Score-based-Diffusion-Model获取。