Learning large-scale vision-language-action (VLA) models from multi-embodiment datasets remains challenging due to heterogeneous action spaces across end effectors. Although latent action models (LAMs) can learn embodiment-agnostic action representations from diverse video data, existing image-based LAMs often fail to capture fine-grained end-effector articulation, particularly finger-level geometric changes in human and dexterous robot hands. To address this limitation, we propose GALA, a Geometry-Aware Latent-Action modeling framework that augments image-based latent actions with 3D end-effector geometric motion. However, naively incorporating point clouds yields fine-grained action representations with limited shared semantics, hindering cross-embodiment pretraining. To address this issue, we introduce the Unified End-effector Motion Representation (UEMR), which preserves fine-grained motion information while improving the cross-embodiment generalizability of latent actions. Building upon UEMR, GALA combines visual latent actions that capture scene-level dynamics with geometric latent actions that capture shared fine-grained end-effector articulation, providing effective supervision for VLA pretraining from multi-embodiment data, including action-free ego-centric human videos. Experiments on fine-grained motion probing, cross-embodiment retrieval, and downstream VLA evaluation demonstrate GALA's effectiveness in modeling generalizable fine-grained motions across embodiments, achieving 68.3% RoboCasa-GR1 success rate and 75.5% real-world success rate. Code, appendix, and demos are available at https://puzhenyuan.github.io/GALA-website/.
Figures & tables
Fig. 1: Overview of GALA . Geometry complements image-based latent actions with generalizable fine-grained end-effector motion, enabling more shared manipulation semantics across heterogeneous end-effectors, therefore enhancing VLA pretraining performance across embodiments.
Fig. 2: Geometry-aware latent-action learning . GALA jointly learns visual and geometric latent actions, with UEMR encouraging geometric latents to represent transferable end-effector transitions across embodiments.
Fig. 3: Geometry-aware VLA co-training. Frozen GALA latents supervise dedicated VLM bridge tokens, while a shared action expert is grounded into embodiment-specific native action spaces.