High-dimensional manipulator operation in unstructured environments requires a differentiable, scene-agnostic distance query mechanism to guide safe motion generation. Existing geometric collision checkers are typically non-differentiable, while workspace-based implicit distance models are hindered by the highly nonlinear workspace--configuration mapping and often suffer from poor convergence; moreover, self-collision and environment collision are commonly handled as separate constraints. We propose Configuration-Space Signed Distance Field-Net (CSSDF-Net), which learns a continuous signed distance field directly in configuration space to provide joint-space distance and gradient queries under a unified geometric notion of safety. To enable zero-shot generalization without environment-specific retraining, we introduce a spatial-hashing-based data generation pipeline that encodes robot-centric geometric priors and supports efficient retrieval of risk configurations for arbitrary obstacle point sets. The learned distance field is integrated into safety-constrained trajectory optimization and receding-horizon MPC, enabling both offline planning and online reactive avoidance. Experiments on a planar arm and a 7-DoF manipulator demonstrate stable gradients, effective collision avoidance in static and dynamic scenes, and practical inference latency for large-scale point-cloud queries, supporting deployment in previously unseen environments.