Signed Distance Fields (SDFs) are a fundamental representation in robot motion planning. Their configuration-space counterpart, the Configuration Space Distance Field (CDF), directly encodes distances in joint space, offering a unified representation for optimization and control. However, existing CDF formulations face two major challenges in high-degree-of-freedom (DoF) robots: (1) they effectively return only a single nearest collision configuration, neglecting the multi-modal nature of minimal-distance collision configurations and leading to gradient ambiguity; and (2) they rely on sparse sampling of the collision boundary, which often fails to identify the true closest configurations, producing oversmoothed approximations and geometric distortion in high-dimensional spaces. We propose CDFlow, a novel framework that addresses these limitations by learning a continuous flow in configuration space via Neural Ordinary Differential Equations (Neural ODEs). We redefine the problem from finding a single nearest point to modeling the distribution of minimal-distance collision configurations. We also introduce an adaptive refinement sampling strategy to generate high-fidelity training data for this distribution. The resulting Neural ODE implicitly models this multi-modal distribution and produces a smooth, consistent gradient field-derived as the expected direction towards the distribution-that mitigates gradient ambiguity and preserves sharp geometric features. Extensive experiments on high-DoF motion planning tasks demonstrate that CDFlow significantly improves planning efficiency, trajectory quality, and robustness compared to existing CDF-based methods, enabling more robust and efficient planning for collision-aware robots in complex environments.