ODEWorld: A Continuous Predictive Architecture via Physical-Time Flow

In the physical world we inhabit, space and time are fundamentally continuous. However, existing machine learning paradigms for world modeling are largely confined to discrete-time prediction and inference, thereby exhibiting significant inefficiency in capturing the fundamental dynamics of the physical world. To bridge this gap, we introduce Physical-Time Flow (PT-Flow), a novel approach that learns a continuous latent velocity field operating in physical time. Crucially, the underlying dynamics of sequential data are parameterized by an ordinary differential equation (ODE) embedded in a well-structured dynamical representation space. Under this paradigm, the prediction of the future can be recast as temporal integration via an ODE solver in the compressed latent space. Building upon PT-Flow, we construct ODEWorld, a physics-grounded, continuous-time latent world model that is both efficient and versatile. By extracting time-variant features and enforcing ODE properties on both the dynamical representation space and the latent velocity field, ODEWorld effectively addresses the long-standing representation collapse issue in latent world model literature. This also enables high-quality image reconstruction with ODEWorld even after long-horizon prediction. Moreover, its continuous nature allows for arbitrary temporal resolution and even backward prediction, which is impossible for most discrete-time models. Lastly, benefiting from the learned dynamics-centric latent space, ODEWorld can provide rich planning-oriented information to facilitate downstream policy learning. Comprehensive experiments across multiple simulation and real-world datasets demonstrate that ODEWorld successfully reconciles planning-conducive dynamics abstraction with visual realism, excelling in both video generation and robotic control. More qualitative results can be found at Project Website.