4D-WAM: Infusing Spatiotemporal Awareness into World Action Models through Trajectory Fields

World action models (WAMs) have recently shown promise in jointly modeling future observations and executable robot actions. However, most existing WAMs still operate in 2D video or latent spaces, where visually plausible rollouts miss the 3D spatial constraints and occluded contact geometry required for precise manipulation. While geometric foundation models offer strong priors for recovering dense 3D structure and motion from visual observations, forcing WAMs to predict the dense 4D representation introduces costly geometric decoding and slows down causal action generation. To address the trade-off, we present WAM4D, a fast 4D world action model that uses lightweight spatial register tokens as training-time future-depth readouts to transfer pretrained geometric priors into a causal video-action transformer, then removes the register branch for lightweight action inference. To prevent non-causal shortcuts, we further design causal mixture attention for the Mixture-of-Transformers (MoT) WAM backbone, defining modality-specific visibility among video, action, and geometry tokens. Comprehensive experiments on RoboTwin 2.0 and challenging real-world manipulation tasks show that WAM4D improves spatial consistency and achieves competitive action prediction while maintaining efficient inference.

World Action Models (WAMs) have emerged as a promising paradigm for robot control by modeling physical dynamics. Current WAMs generally follow two paradigms: the "Imagine-then-Execute" approach, which uses video prediction to infer actions via inverse dynamics, and the "Joint Modeling" approach, which jointly models actions and video representations. Based on systematic experiments, we observe a fundamental trade-off between these paradigms: the former explicitly leverages world models for generalizable transit but lacks interaction precision, whereas the latter enables fine-grained, temporally coherent action generation but is constrained by the exploration space of the training distribution. Motivated by these findings, we propose HarmoWAM, an end-to-end WAM that fully leverages a world model to unify predictive and reactive control, enabling both generalizable transit and precise manipulation. Specifically, the world model provides spatio-temporal physical priors that condition two complementary action experts: a predictive expert that leverages latent dynamics for iterative action generation, and a reactive expert that directly infers actions from predicted visual evolution. To enable adaptive coordination, a Process-Adaptive Gating Mechanism is proposed to automatically determine the timing and location of switching between them. This allows the world model to drive the reactive expert to expand the exploration space and the predictive expert to perform precise interactions across different stages of a task. For evaluation, we construct three training-unseen test environments across six real-world robotic tasks, covering variations in background, position, and object semantics. Notably, HarmoWAM achieves strong zero-shot generalization across these scenarios, significantly outperforming prior state-of-the-art VLA models and WAMs by margins of 33% and 29%, respectively.

We propose X-WAM, a Unified 4D World Model that unifies real-time robotic action execution and high-fidelity 4D world synthesis (video + 3D reconstruction) in a single framework, addressing the critical limitations of prior unified world models (e.g., UWM) that only model 2D pixel-space and fail to balance action efficiency and world modeling quality. To leverage the strong visual priors of pretrained video diffusion models, X-WAM imagines the future world by predicting multi-view RGB-D videos, and obtains spatial information efficiently through a lightweight structural adaptation: replicating the final few blocks of the pretrained Diffusion Transformer into a dedicated depth prediction branch for the reconstruction of future spatial information. Moreover, we propose Asynchronous Noise Sampling (ANS) to jointly optimize generation quality and action decoding efficiency. ANS applies a specialized asynchronous denoising schedule during inference, which rapidly decodes actions with fewer steps to enable efficient real-time execution, while dedicating the full sequence of steps to generate high-fidelity video. Rather than entirely decoupling the timesteps during training, ANS samples from their joint distribution to align with the inference distribution. Pretrained on over 5,800 hours of robotic data, X-WAM achieves 79.2% and 90.7% average success rate on RoboCasa and RoboTwin 2.0 benchmarks, while producing high-fidelity 4D reconstruction and generation surpassing existing methods in both visual and geometric metrics.