PermVLA: Factorization Order as a Regularizer for VLA Learning

Test-time sampling can improve Vision-Language-Action (VLA) policies, but only if the model can efficiently select a good action from multiple candidates. Prior work often relies on separately trained external verifiers, adding extra models and inference overhead. We propose Token Probability Bucketing (TokenPB), a self-verification approach that discretizes continuous action chunks into bucket tokens and co-trains a single VLA checkpoint with a joint objective: a flow-matching loss for action generation and an auxiliary bucket loss $\mathcal{L}_{\text{bucket}}$ that teaches the VLM backbone to model observation-conditioned distributions over bucket-token sequences. At inference, TokenPB samples $M$ candidates, scores each via teacher-forced evaluation under the learned distribution, and selects the best---enabling efficient batched scoring with observation-prefix KV-cache reuse. We provide theory connecting the training objective to a monotonic ranking property and bounds on expected selection regret that separate candidate-set effects from calibration. Across multiple backbones and benchmarks, TokenPB yields consistent success-rate improvements over single-sample inference from the same checkpoint (+2.7 in simulation, +17.1 in real-world, +16.4 under out-of-distribution shifts), and further improves over external-verifier baselines under the same sampling budget. The code is publicly available at https://github.com/RUCKBReasoning/TokenPB.

Vision-Language-Action (VLA) models that couple pretrained Vision-Language Models (VLMs) with continuous action experts have achieved strong manipulation performance, yet generalization to out-of-distribution (OOD) language instructions remains poor. A known challenge is the structural imbalance in VLA data, where language is far less diverse than visual and action content, making policies prone to visual shortcuts. While discrete-action methods mitigate this through vision-language co-training, continuous action experts lack such protection: they start from random initialization and learn entirely from imbalanced data, producing noisy gradients that corrupt the VLM and fail to exploit its language capability. We address this from a Bayesian perspective, factorizing the policy into a language-agnostic Vision-Action (VA) prior and a language-conditioned VLA likelihood, and propose APT, a two-stage training method emphasizing Action expert PreTraining. In Stage 1, the action expert is pretrained as a VA prior on vision-action pairs from a frozen VLM, bypassing the language imbalance. In Stage 2, language tokens are injected through a gated fusion mechanism that integrates VLM features while preserving the learned visuomotor prior. APT applies to mainstream VLA architectures, including the $π$ and GR00T-style architectures. Comprehensive experiments validate that APT achieves consistent gains on unseen instructions and compositional tasks. Project Page: https://xukechun.github.io/papers/APT/

Flow-based Vision-Language-Action (VLA) policies are inherently stochastic: different noise seeds can produce action chunks of varying quality from the same observation. At test time, however, the policy typically commits to a single sample without an explicit estimate of its quality. In fine-grained manipulation, executing a suboptimal action can irreversibly disrupt task progress and lead to failure. To exploit policy stochasticity, we introduce a training-free two-axis trigger that uses two initial samples to measure within-chunk temporal variation and cross-sample variance, detecting the critical states. Once triggered, a JEPA-based latent world model ranks candidate action chunks by predicting action-conditioned future latent states and the corresponding changes in task progress. By operating in latent space, the verifier avoids pixel reconstruction and enables efficient and more accurate ranking. Across three real-world tasks, $\textit{i.e.,}$ pen insertion, pipetting, and apple placement), our method raises the average completion score from 50.8% to 65.5%, while adding 326 ms for sampling and verification per triggered decision on a single RTX 4090. Consistent gains are also observed in simulation, where the average success rate rises from 66.4% to 73.6% in the clean setting of RoboTwin 2.0, from 62.8% to 69.6% in its randomized setting, and from 96.9% to 97.6% on LIBERO.