# Geometry-Privileged Distillation

Vision-language models struggle with spatial reasoning because RGB inputs do not directly supply geometric evidence, and existing fixes either add 3D at inference, paying architecture and latency costs, or train on outcome rewards that supervise only the final answer. GPD renders depth, semantic segmentation and bird's-eye-view layout as compact text, routes the question-relevant subset to the teacher alongside the reference answer, and applies a privileged KL only to incorrect trajectories within GRPO, leaving the deployed model RGB-only. On the 4B backbone it reaches 57.1 on VSI-Bench and 37.6 average across MindCube, SPAR-Bench, MMSI-Bench and ViewSpatial, above GRPO and answer-privileged OPSD.

Vision-language models struggle with spatial reasoning because RGB inputs do not directly supply geometric evidence, and existing fixes either add 3D at inference, paying architecture and latency costs, or train on outcome rewards that supervise only the final answer. GPD renders depth, semantic segmentation and bird's-eye-view layout as compact text, routes the question-relevant subset to the teacher alongside the reference answer, and applies a privileged KL only to incorrect trajectories within GRPO, leaving the deployed model RGB-only. On the 4B backbone it reaches 57.1 on VSI-Bench and 37.6 average across MindCube, SPAR-Bench, MMSI-Bench and ViewSpatial, above GRPO and answer-privileged OPSD.