SymVD: Symmetric Vision Language Action Distillation for Robot Manipulation

While pretrained Vision-Language-Action (VLA) models offer broad generalization capabilities in robotic manipulation tasks, adapting them to real-world environments or handling task shifts often requires substantial additional data and retraining. To address this, we propose Symmetric VLA Distillation (SymVD), a distillation framework that transfers knowledge from a large VLA teacher to a compact student policy by explicitly exploiting geometric symmetries in manipulation tasks, such as rotational and reflectional invariance. SymVD employs an equivariant actor-critic architecture and trains the student using a symmetry-aware objective that aligns with teacher actions under group-invariant properties. We demonstrate that by enforcing the policy to respect equivariance, SymVD reduces redundant exploration across configurations related by group transformations and improves sample efficiency during distillation. To further stabilize and improve distillation, SymVD introduces an adaptive weighting scheme that dynamically balances the distillation objective and reinforcement learning updates based on training progress, enabling robust transfer even when the teacher signal is imperfect or misaligned. Experimental results on robotic manipulation tasks demonstrate that SymVD consistently improves over standard distillation and also outperforms SAC in terms of sample efficiency and generalization to previously unseen symmetric transformations of the environment.