Current visual navigation strategies mainly follow an exploration-first and then goal-directed navigation paradigm. This exploratory phase inevitably compromises the overall efficiency of navigation. Recent studies propose leveraging floor plans alongside RGB inputs to guide agents, aiming for rapid navigation without prior exploration or mapping. Key issues persist despite early successes. The modal gap and content misalignment between floor plans and RGB images necessitate an efficient approach to extract the most salient and complementary features from both for reliable navigation. Here, we propose GlocDiff, a novel framework that employs a diffusion-based policy to continuously predict future waypoints. This policy is conditioned on two complementary information streams: (1) local depth cues derived from the current RGB observation, and (2) global directional guidance extracted from the floor plan. The former handles immediate navigation safety by capturing surrounding geometry, while the latter ensures goal-directed efficiency by offering definitive directional cues. Extensive evaluations on the FloNa benchmark demonstrate that GlocDiff achieves superior efficiency and effectiveness. Furthermore, its successful deployment in real-world scenarios underscores its strong potential for broad practical application.