Abstract
World action models (WAMs) provide a promising learning paradigm for robotic manipulation by jointly modeling future observations and robot actions. However, most existing methods operate in 2D image spaces, making it difficult to explicitly capture spatial scene dynamics, maintain cross-view geometric consistency, and effectively align visual observations with robot actions. To address this, we propose GSWAM, a world action model based on 3D Gaussian Splatting (3DGS), which jointly models scene dynamics and robot actions in a unified 3D space. We first compress 3DGS scenes into geometrically consistent latent representations using a Gaussian variational autoencoder (GSVAE). Furthermore, we align scenes and actions within a shared 3D-anchored space, enabling GSWAM to explicitly model the joint distribution between 3D scene dynamics and robot actions. Based on this representation, we design a 3D-anchor-based spatial diffusion transformer to model spatial interactions between scenes and actions. To accommodate their different generative characteristics, we further employ decoupled flow timesteps for the two modalities, allowing the model to jointly learn scene-action generation and action-conditioned future scene prediction. Experiments on both simulated and real-world robotic manipulation tasks demonstrate that GSWAM outperforms representative existing methods in both action generation and future scene prediction.