Multi-agent path planning is a central challenge in areas such as robotics, autonomous vehicles, and swarm intelligence. Traditional discrete methods often struggle with real-time adaptability and computational efficiency, emphasizing the need for continuous, optimizable solutions. This paper introduces a novel approach that harnesses Neural Ordinary Differential Equations (Neural ODEs) for multi-agent path planning in a continuous-time framework. By parameterizing agent dynamics using neural networks within these ODEs, we enable end-to-end trajectory optimization. The inherent dynamics of ODEs facilitate collision avoidance. We demonstrate our method's effectiveness across both 2D and 3D scenarios, navigating multiple agents amidst obstacles, underscoring the potential of Neural ODEs to transform path planning.