# Quantile Head for Vision-Language-Action Models

arXiv: https://arxiv.org/abs/2609.34061 · HTML: https://mlsanity.com/paper/2609.34061/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Embodied and 3D vision-language models, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 28 of its 34 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

- Multimodal LLMs / vision-language models / [Embodied and 3D vision-language models](https://mlsanity.com/mllm/embodied-and-3d-vision-language-models/)
- Vision-language-action models / [Efficient VLA inference and adaptation](https://mlsanity.com/vla/efficient-vla-inference-and-adaptation/)
- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 28 of 28)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [LIBERO: Benchmarking Knowledge Transfer for Lifelong Robot Learning](https://mlsanity.com/paper/2306.03310/) (2023)
- [Fine-Tuning Vision-Language-Action Models: Optimizing Speed and Success](https://mlsanity.com/paper/2502.19645/) (2025)
- [FAST: Efficient Action Tokenization for Vision-Language-Action Models](https://mlsanity.com/paper/2501.09747/) (2025)
- [X-VLA: Soft-Prompted Transformer as Scalable Cross-Embodiment Vision-Language-Action Model](https://mlsanity.com/paper/2510.10274/) (2025)
- [MolmoAct: Action Reasoning Models that can Reason in Space](https://mlsanity.com/paper/2508.07917/) (2025)
- [MemoryVLA: Perceptual-Cognitive Memory in Vision-Language-Action Models for Robotic Manipulation](https://mlsanity.com/paper/2508.19236/) (2025)
- [LIBERO-PRO: Towards Robust and Fair Evaluation of Vision-Language-Action Models Beyond Memorization](https://mlsanity.com/paper/2510.03827/) (2025)
- [VLA-Adapter: An Effective Paradigm for Tiny-Scale Vision-Language-Action Model](https://mlsanity.com/paper/2509.09372/) (2025)
- [ACoT-VLA: Action Chain-of-Thought for Vision-Language-Action Models](https://mlsanity.com/paper/2601.11404/) (2026)
- [InternVLA-A1.5: Unifying Understanding, Latent Foresight, and Action for Compositional Generalization](https://mlsanity.com/paper/2607.04988/) (2026)
- [SnapFlow: One-Step Action Generation for Flow-Matching VLAs via Progressive Self-Distillation](https://mlsanity.com/paper/2604.05656/) (2026)
- [World-Language-Action Model for Unified World Modeling, Language Reasoning, and Action Synthesis](https://mlsanity.com/paper/2606.05979/) (2026)
- [Geometric Action Model for Robot Policy Learning](https://mlsanity.com/paper/2606.17046/) (2026)
- [SimVLA: A Simple VLA Baseline for Robotic Manipulation](https://mlsanity.com/paper/2602.18224/) (2026)
- [MemoryVLA++: Temporal Modeling via Memory and Imagination in Vision-Language-Action Models](https://mlsanity.com/paper/2606.09827/) (2026)
- [ReconVLA: An Uncertainty-Guided and Failure-Aware Vision-Language-Action Framework for Robotic Control](https://mlsanity.com/paper/2604.16677/) (2026)
- [GE-Act 2.0: Pretraining and Scaling a World-Action Model for Robotic Manipulation](https://mlsanity.com/paper/2609.05588/) (2026)
- [Let It Be Simple: One-Step Action Generation for Vision-Language-Action Models](https://mlsanity.com/paper/2606.05737/) (2026)
- [OrderFusion: Encoding Orderbook for End-to-End Probabilistic Intraday Electricity Price Forecasting](https://mlsanity.com/paper/2502.06830/) (2025)
- [Continuous Reasoning for Vision-Language-Action](https://mlsanity.com/paper/2606.00229/) (2026)
- [SUREFlow: State-space Uncertainty-aware REsidual Flow Matching for Robust Robot Manipulation](https://mlsanity.com/paper/2607.10504/) (2026)
- [CofactVLA: Deconfounding Vision-Language-Action Models via Counterfactual Intervention](https://mlsanity.com/paper/2608.04396/) (2026)

## Abstract (arXiv)

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 episode time among matched LIBERO baselines; code is available at https://github.com/xwangrs/Quantile-Head-for-VLA.