We propose a Geometry-aware Policy Imitation (GPI) approach that rethinks imitation learning by treating demonstrations as geometric curves rather than collections of state-action samples. From these curves, GPI derives distance fields that give rise to two complementary control primitives: a progression flow that advances along expert trajectories and an attraction flow that corrects deviations. Their combination defines a controllable, non-parametric vector field that directly guides robot behavior. This formulation decouples metric learning from policy synthesis, enabling modular adaptation across low-dimensional robot states and high-dimensional perceptual inputs. GPI naturally supports multimodality by preserving distinct demonstrations as separate models and allows efficient composition of new demonstrations through simple additions to the distance field. We evaluate GPI in simulation and on real robots across diverse tasks. Experiments show that GPI achieves higher success rates than diffusion-based policies while running 20 times faster, requiring less memory, and remaining robust to perturbations. These results establish GPI as an efficient, interpretable, and scalable alternative to generative approaches for robotic imitation learning. Project website: https://yimingli1998.github.io/projects/GPI/

翻译：我们提出了一种几何感知策略模仿（GPI）方法，该方法通过将示范视为几何曲线而非状态-动作样本的集合来重新思考模仿学习。GPI从这些曲线推导出距离场，从而产生两种互补的控制基元：一种沿专家轨迹推进的推进流，以及一种纠正偏差的吸引流。它们的组合定义了一个可控的、非参数化的向量场，可直接指导机器人行为。该公式将度量学习与策略合成解耦，实现了跨低维机器人状态和高维感知输入的模块化适配。GPI通过将不同的示范保留为独立的模型，自然地支持多模态，并允许通过对距离场进行简单加法来高效组合新的示范。我们在仿真和真实机器人上针对多种任务评估了GPI。实验表明，GPI比基于扩散的策略实现了更高的成功率，同时运行速度快20倍，所需内存更少，并且对扰动保持鲁棒性。这些结果确立了GPI作为机器人模仿学习中生成式方法的一种高效、可解释且可扩展的替代方案。项目网站：https://yimingli1998.github.io/projects/GPI/