Quantile Head for Vision-Language-Action Models

Xuan Wang, Yinan Wu, Haoran Duan, Jungong Han

Vision-Language-Action (VLA) models integrate pretrained Vision-Language Models (VLMs) with action heads for robot control. Common action heads have distinct limitations: point regression provides only a point estimate of the action distribution, while standard flow-matching samplers require costly iterative sampling. To address these limitations, we unify regression and flow matching under a shared objective and extend it to derive a quantile objective. This quantile objective guides the design of our Quantile Head, which predicts a median and positive gaps to form ordered marginal action quantiles in one forward pass. These quantiles support multiple sampling strategies without retraining and are jointly supervised to train the default median policy. Our local analysis of this joint supervision shows that, with calibrated nearby quantiles, fixed gaps, and matched correction speed, direct median updates have lower variance than under median-only supervision. Experiments show that this jointly supervised median policy achieves the highest average success rates among the compared methods on LIBERO, LIBERO-Plus, LIBERO-Pro, and two real-robot tasks, together with the shortest mean…