ODEWorld: A Continuous Predictive Architecture via Physical-Time Flow

2026-07-30

AI Summary

This work addresses the limitations of existing world models, which predominantly rely on discrete-time prediction and struggle to accurately capture the continuous spatiotemporal dynamics of the physical world. The authors propose Physical-Time Flow (PT-Flow), introducing ODEWorld—the first continuous implicit world model grounded in physical time. ODEWorld models a latent velocity field governed by ordinary differential equations (ODEs) within a structured latent space, casting future prediction as a time integration process in that space. This formulation mitigates representation collapse, enables predictions at arbitrary temporal resolutions, supports backward-in-time inference, and provides rich temporal information for planning. Experiments demonstrate that ODEWorld maintains high visual fidelity in long-horizon video generation, significantly outperforming discrete-time baselines, and effectively facilitates downstream policy learning tasks such as robotic control.

Abstract

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, thereby exhibiting significant inefficiency in capturing the dynamics of physical world. We introduce Physical-Time Flow (\textbf{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 representation space. Under this paradigm, the prediction of future can be recast as temporal integration via an ODE solver in the compressed latent space. Building upon PT-Flow, we construct \textbf{ODEWorld}, a 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 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, ODEWorld can provide rich planning-oriented information to facilitate downstream policy learning. Comprehensive experiments demonstrate that ODEWorld successfully reconciles planning-conducive dynamics abstraction with visual realism, excelling in both video generation and robotic control. \href{https://dstate.github.io/odeworld_website/}{Project Website}.

Problem

• continuous-time modeling
• world model
• latent dynamics
• representation collapse
• physical-time prediction

Innovation

• Continuous-time modeling
• Ordinary Differential Equation (ODE)
• Latent world model
• Physical-Time Flow
• Temporal integration