# Transport Discrepancy as a Reliability Signal for Vision-Language-Action Models

arXiv: https://arxiv.org/abs/2512.01715 · HTML: https://mlsanity.com/paper/2512.01715/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Efficient VLA inference and adaptation, one of 13 directions in Vision-language-action models.
- Builds on 52 of its 64 references that are in the map.
- First posted on arXiv 1 Dec 2025.

## Placed in

- 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, 30 of 52)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Improved Baselines with Visual Instruction Tuning](https://mlsanity.com/paper/2310.03744/) (2023)
- [Flamingo: a Visual Language Model for Few-Shot Learning](https://mlsanity.com/paper/2204.14198/) (2022)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [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)
- [MiniGPT-4: Enhancing Vision-Language Understanding with Advanced Large Language Models](https://mlsanity.com/paper/2304.10592/) (2023)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [PaLM-E: An Embodied Multimodal Language Model](https://mlsanity.com/paper/2303.03378/) (2023)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World](https://mlsanity.com/paper/1703.06907/) (2017)
- [Octo: An Open-Source Generalist Robot Policy](https://mlsanity.com/paper/2405.12213/) (2024)
- [LIBERO: Benchmarking Knowledge Transfer for Lifelong Robot Learning](https://mlsanity.com/paper/2306.03310/) (2023)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [GR00T N1: An Open Foundation Model for Generalist Humanoid Robots](https://mlsanity.com/paper/2503.14734/) (2025)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Fine-Tuning Vision-Language-Action Models: Optimizing Speed and Success](https://mlsanity.com/paper/2502.19645/) (2025)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)

## Built on by (most cited first, 6 of 6)

- [Being-H0.5: Scaling Human-Centric Robot Learning for Cross-Embodiment Generalization](https://mlsanity.com/paper/2601.12993/) (2026)
- [ImageWAM: Do World Action Models Really Need Video Generation, or Just Image Editing?](https://mlsanity.com/paper/2606.19531/) (2026)
- [LARA: Latent Action Representation Alignment for Vision-Language-Action Models](https://mlsanity.com/paper/2606.07100/) (2026)
- [Human-Centric Transferable Tactile Pre-Training for Dexterous Robotic Manipulation](https://mlsanity.com/paper/2607.01067/) (2026)
- [Escaping the Diversity Trap in Robotic Manipulation via Anchor-Centric Adaptation](https://mlsanity.com/paper/2605.07381/) (2026)
- [PearlVLA: Progressive Embodied Action-Plan Refinement in Latent Space](https://mlsanity.com/paper/2606.17924/) (2026)

## Abstract (arXiv)

Vision-language-action (VLA) models that generate continuous action chunks via flow matching lack an internal signal for judging whether a given prediction is reliable. Distribution shift and long-horizon rollouts can push backbone representations away from the region the action head decodes reliably, yet the policy has no mechanism to detect or react to this drift. We observe that the cost of transporting observation features to the action representation in a shared feature space rises precisely when such drift occurs, providing a per-step reliability estimate without extra supervision. Building on this observation, we propose DiG (Discrepancy Gate), a lightweight plug-in module for flow-matching VLA policies. DiG computes a sliced Wasserstein transport cost between backbone features and the action expert's own input projection, maps it through an exponential gate, and uses the gate to modulate both a residual feature refinement and the training loss. At inference time, the gate enables DiG-Refinefine, an iterative refinement process that corrects action chunks before execution. Experiments on both simulation and real-world scenarios show that DiG consistently improves success rates, with the largest gains under distribution shift and on long-horizon tasks.