Continuous-Action World Models: Learning Cross-Embodiment Spatiotemporal Dynamics Priors

The diversity of robot embodiments and action spaces makes it challenging to build robot world models that generalize across different embodiments. We introduce the Latent Action-Conditioned Robot World Model (LAC-WM), which operates within a learned unified latent action space shared across diverse embodiments. This unified action space improves the world model's performance when adapted to previously unseen robot embodiments. We compare LAC-WM with an Explicit Action-Conditioned World Model (EAC-WM), which conditions on explicit motion labels. Our results show that explicit action conditioning leads to disjoint action representations across embodiments, limiting downstream performance when adapting to new robots. We evaluate both models on dexterous manipulation tasks and a modified LIBERO benchmark. LAC-WM improves downstream performance over EAC-WM by up to 46.7% on dexterous manipulation and 11.7% on LIBERO. Crucially, the unified latent action space allows LAC-WM's downstream performance to scale positively with the number of embodiments used during pretraining. In contrast, the disjoint action space in EAC-WM leads to decreased performance as the number of pretraining embodiments increases. These results highlight the importance of a unified action space for efficient cross-embodiment learning, addressing a key challenge in robotics. Project website: https://lacwm.github.io/

Predicting the next state is a core paradigm of World Models for modeling physical dynamics, emphasizing prediction fidelity. As World Models evolve into World-Action Models (WAMs), existing methods still fix the next state before training as RGB, a single latent feature, or a static combination of predefined targets, thereby constraining action learning to the inductive biases preserved by a particular representation. To address this limitation, we propose CF-WAM, a dynamic next-state prediction framework that samples visual, semantic, geometric, and interaction projections of the same future, standardizes them into a common video form, and supervises a unified WAM across these projections. The action-relevant constraints exposed by these projections accumulate across training steps, forcing WAM to capture the underlying state-transition structure that supports multiple projections of the same action-conditioned future. This dynamic mechanism also provides a natural cross-embodiment dynamics reference frame for Human and Robot learning. By jointly learning across different next-state parameterizations, heterogeneous Human and Robot experience can bypass appearance differences and directly contribute to shared state-transition learning, improving cross-embodiment generalization. Experiments show that CF-WAM improves both training efficiency and final control performance, while translating Human experience effectively into policy gains. CF-WAM achieves state-of-the-art performance on RoboCasa-GR1 with an average success rate of 82.50%, while reaching 82.65% on LIBERO-Plus and up to 84.00% in real-world evaluations.

We introduce Riemann-1.0, a fully causal autoregressive World Action Model for embodied intelligence. Riemann-1.0 jointly models multi-view visual observations, robot states, and embodiment-specific actions within a unified causal autoregressive sequence, representing robot actions and world evolution as causal state transitions. Unlike existing WAMs based on joint generation, video-first prediction, or decoupled modeling paradigms, Riemann-1.0 unifies online robot policy execution and action-conditioned world simulation within a single model, enabling it to function as both an executable robot policy and a multi-embodiment visual world simulator. To scale embodied experience across heterogeneous data sources, we further develop a progressive embodied pretraining framework that unifies learning from egocentric human videos, handheld-gripper demonstrations, and heterogeneous robot trajectories under a shared World Action Modeling objective. Built upon 200K+ hours of interaction data, Riemann-1.0 progressively transfers large-scale embodied experience into executable robot manipulation capabilities. Riemann-1.0 achieves state-of-the-art performance across both simulation benchmarks and real-world manipulation tasks. It achieves success rates of 94.3% on RoboTwin2.0, 99.0% on LIBERO, and 62.6% on the long-horizon compositional benchmark RoboCasa-365, outperforming the previous best method by 8.4% On long-horizon real-world manipulation tasks, Riemann-1.0 achieves a Success Rate (SR) of 85.0% and a Progress Success Rate (PSR) of 94.4%, exceeding the strongest open-source baseline by 15% in SR. These results demonstrate that unified World Action Modeling together with progressive embodied pretraining effectively transforms large-scale embodied experience into generalizable robot manipulation capabilities.