ODEWorld：一種基於物理時間流之連續式預測架構

摘要

在我們所處的物理世界中，空間與時間從根本上是連續的。然而，現有的世界建模機器學習範式大多受限於離散時間預測，因此在捕捉物理世界動態方面表現出顯著的低效。我們提出了物理時間流（PT-Flow），一種新穎的方法，學習在物理時間中運作的連續潛在速度場。關鍵在於，序列數據的底層動態由一個嵌入於結構良好的表徵空間中的常微分方程（ODE）所參數化。在此範式下，未來的預測可以重新表述為透過ODE求解器在壓縮潛在空間中進行時間積分。基於PT-Flow，我們構建了ODEWorld，一個既高效又多用途的連續時間潛在世界模型。透過提取時變特徵並在動態表徵空間與潛在速度場上強制實施ODE性質，ODEWorld有效解決了潛在世界模型文獻中長期存在的表徵坍縮問題。這也使得即使在長期預測之後，仍能實現高品質的影像重建。此外，其連續性允許任意的時間解析度，甚至能進行反向預測，而這對大多數離散時間模型而言是不可能的。最後，ODEWorld能提供豐富的、有助於規劃的資訊，以促進下游策略學習。綜合實驗表明，ODEWorld成功調和了有利於規劃的動態抽象與視覺真實性，在影片生成和機器人控制方面均表現出色。https://dstate.github.io/odeworld_website/{Project Website}。

English

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 (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 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. https://dstate.github.io/odeworld_website/{Project Website}.