WSA${}_1$: a 3D-Centric World-Spatial-Action Model for Generalizable Robot Control

World-Action Models (WAMs) have emerged as a promising paradigm for robot control by using predicted world evolution to guide action generation. However, existing WAMs largely follow a one-way world-to-action paradigm. Real-world interaction, in contrast, is inherently driven by bidirectional temporal causality with implicit physics: the evolving world informs what actions should be taken, while the executed actions, in turn, determine how the world evolves. Without explicitly modeling this action-to-world direction, WAMs cannot assess whether the consequences of their generated actions align with the world evolution they predict, preventing WAMs from capturing consistent interaction dynamics from video demonstrations and thereby constraining their generalization capabilities in real-world scenarios. In this paper, we introduce WSA${}_1$, a new modeling paradigm for embodied foundation models. WSA${}_1$ develops a World-Spatial-Action understanding by jointly modeling three interconnected processes: how actions transform the 3D world (world level), how spatial states evolve toward desired outcomes (spatial level), and how target 3D world guide appropriate robot behaviors (action level). By integrating these processes, WSA${}_1$ enables a more coherent and tightly coupled understanding of embodied interactions. Compared with prior WAMs trained on tens of thousands of hours of real-robot data, WSA${}_1$ leverages 6k hours of video demonstrations (only 1k from real robot), demonstrating strong data efficiency. Moreover, even our 3B-parameter WSA${}_1$ surpasses larger WAMs with 6B–8B parameters, highlighting its parameter efficiency. Experiments show that WSA${}_1$ achieves a 93.3% success rate on RoboTwin2.0, delivering an average 20% improvement over state-of-the-art models on real-world OOD robot control tasks.