ODEWorld：一种基于物理时间流的连续预测架构

摘要

在我们所处的物理世界中，空间和时间本质上是连续的。然而，现有的世界建模机器学习范式大多局限于离散时间预测，因此在捕捉物理世界动态方面表现出显著的低效。我们引入了物理时间流（PT-Flow），一种学习在物理时间中运行的连续潜在速度场的新方法。关键在于，序列数据的底层动态由一个嵌入在结构化良好的表示空间中的常微分方程（ODE）进行参数化。在该范式下，未来预测可以被重新表述为在压缩潜在空间中通过ODE求解器进行时间积分。基于PT-Flow，我们构建了ODEWorld，一种既高效又通用的连续时间潜在世界模型。通过提取时变特征并在动态表示空间和潜在速度场上强制执行ODE属性，ODEWorld有效解决了潜在世界模型文献中长期存在的表示坍缩问题。这也使得即使在长时域预测之后也能实现高质量的图像重建。此外，其连续性允许任意时间分辨率甚至反向预测，这对于大多数离散时间模型来说是不可能的。最后，ODEWorld可以提供丰富的面向规划的信息，以促进下游策略学习。综合实验表明，ODEWorld成功地将利于规划的动力学抽象与视觉真实性相协调，在视频生成和机器人控制方面均表现出色。https://dstate.github.io/odeworld_website/{项目网站}。

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}.