Visual-Advantage On-Policy Distillation for Vision-Language Models

On-policy knowledge distillation has proven effective for language models, yet its application to vision-language models (VLMs) remains underexplored. We observe that standard on-policy distillation can improve a student's output quality while failing to strengthen its reliance on visual input: on vision-critical tokens, the student's predictions remain largely unchanged whether or not fine-grained visual detail is present, even though the teacher's predictions depend heavily on it. To make this difference observable, we introduce visual advantage (VA), the token-level log-probability difference when the teacher scores a student-generated rollout with versus without access to fine-grained visual detail. VA is concentrated in a small minority of tokens, and these high-VA tokens are the ones that actually carry the visual supervision signal. This motivates a distillation objective that treats them differently from language scaffolding, so their contribution is not diluted by the abundant surrounding language tokens. We propose Visual-Advantage On-Policy Distillation (VA-OPD), which uses VA at two granularities: rollout-level reweighting by trajectory-averaged VA, and token-level KL averaged within high-VA and low-VA groups separately. We train on two math datasets (Geometry3K and ViRL-39k) and evaluate on eight benchmarks covering both mathematical reasoning and visual understanding, across three teacher sizes (4B, 8B, and 32B) on the Qwen3-VL family. VA-OPD improves over standard on-policy distillation on every benchmark, with the gain growing monotonically along both the teacher-size and data-scale axes, suggesting that these factors compound consistently.