Robotic Manipulation is Vision-to-Geometry Mapping: Vision-Geometry Backbones over Language and Video Models

At its core, robotic manipulation is a problem of vision-to-geometry mapping (f(v) rightarrow G). Physical actions are fundamentally defined by geometric properties like 3D positions and spatial relationships. Consequently, we argue that the foundation for generalizable robotic control should be a vision-geometry backbone, rather than the widely adopted vision-language or video models. Conventional VLA and video-predictive models rely on backbones pretrained on large-scale 2D image-text or temporal pixel data. While effective, their representations are largely shaped by semantic concepts or 2D priors, which do not intrinsically align with the precise 3D geometric nature required for physical manipulation. Driven by this insight, we propose the Vision-Geometry-Action (VGA) model, which directly conditions action generation on pretrained 3D representations. Specifically, VGA replaces conventional language or video backbones with a pretrained 3D world model, establishing a seamless vision-to-geometry mapping that translates visual inputs directly into physical actions. To further enhance geometric consistency, we introduce Progressive Volumetric Modulation and jointly train action and 3D property prediction to preserve geometric representations. Extensive experiments validate the effectiveness of our approach. Across simulation benchmarks, VGA outperforms leading VLA, 3D-VLA, and WAM baselines, including π0.5, OpenVLA-OFT, GeoVLA, and Motus. In real-world deployments, VGA surpasses π0.5 under unseen viewpoints and accurately follows language instructions for target grasping. These results highlight that operating on native 3D representations, rather than relying primarily on language or video priors, offers a promising direction toward generalizable physical intelligence. Project page: https://hcplab-sysu.github.io/VisionGeometryActionModel.