Real-time navigation in cluttered and dynamic environments requires collision-free and dynamically feasible motion under limited perception. However, feasible navigation behaviors are inherently multimodal because multiple paths may exist around obstacles. In this paper, we formulate navigation as learning a transferable goal-conditioned stochastic path prior that models a reusable distribution over goal-aligned geometry-consistent local paths conditioned on local observations. This formulation enables structured sampling of navigation candidates, allowing multiple feasible paths to be explored through sampling without relying on robot-specific motion constraints. To this end, we introduce a goal-aligned canonical state representation that removes in-plane rotational ambiguity and normalizes local geometry with respect to the goal, enabling rotation-invariant path distribution learning. We further develop a structured prior learning framework that parameterizes local paths using a geometry-aware polar action manifold and incorporates risk-sensitive utility shaping with multi-goal distributional rollouts for stable and safety-aware planning. Extensive experiments in dense static environments and dynamic pedestrian scenarios demonstrate that the proposed method achieves consistently high success rates with competitive efficiency while enabling cross-platform transfer of a single path prior learned on differential-drive robots to quadruped platforms without retraining.