We present HorizonNav, a video diffusion-based framework for anticipatory robot navigation that transforms a single RGB image and a text prompt into a geometrically aligned representation of plausible surrounding 3D space. Given the initial observation and a textual description of the reconstruction objective, a vision-language model, guided by designed instructions, interprets the scene and constructs structured prompts for a video diffusion model. The resulting video sequence provides plausible future observations of the environment, which are subsequently processed using monocular ORB-SLAM3 for camera pose estimation and Video Depth Anything for dense depth prediction. Our central contribution is a geometry-guided depth alignment stage that combines the estimated camera poses with triangulated visual landmarks to constrain dense depth predictions across multiple views. This alignment improves the geometric consistency of the reconstructed 3D environment, addressing inconsistencies that temporal coherence of the generated video alone cannot resolve. The experimental evaluation of navigation in imagined 3D environment shows that across a 19-scene horizon study, planning-feasible scenes increase from 13/19 at P20 to 15/19 at P81, while successful RRT trials increase from 62/90 to 75/90. In a separate corridor study, 6 of 25 evaluable generated-camera trajectories violate the reconstructed collision constraints; RRT planner recovers feasible alternatives in 5 of those 6 cases. A larger archive contains 58 usable reconstructions from 67 attempted cases, of which 36 support a downstream plan and 22 do not, exposing reconstruction and free-space failure modes rather than hiding them without lidar. Across 15 corridor reconstructions, the mean reconstruction error is approximately 0.30 m at matched structural landmarks.

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