World models that capture how actions induce physical change enable scalable robot learning without reliance on embodiment-specific action labels. Pixel-space video models provide broad visual priors but expend model capacity on dense appearance reconstruction, while direct action models require embodiment-specific labels that hinder scalability. We present $μ_0$, a scalable world model based on 3D traces. Rather than predicting dense pixels or directly modeling actions, $μ_0$ forecasts smooth 3D trajectories for salient interaction points such as objects, tools, hands, and contact regions, yielding a compact, embodiment-agnostic motion interface. To enable training from diverse video sources, our TraceExtract system automatically extracts 3D supervision by selecting keypoints, constructing globally aligned traces, and associating motion segments with hierarchical language captions. This TraceExtract supervision pretrains $μ_0$ by combining a pretrained vision-language backbone with a modular trace expert, which represents each query via B-spline control points and predicts future traces. Experiments show that $μ_0$ outperforms baselines in both 2D and 3D trace prediction, including trace prediction models and tokenized VLM methods. Because $μ_0$ is frozen and reusable, it can be paired with action experts for downstream robot embodiments. Despite action-free pretraining, the resulting trace-conditioned policies achieve performance competitive with VLA models pretrained with action supervision, such as $π_0$. These results establish 3D traces as a scalable and transferable representation for cross-embodiment manipulation.

翻译：能捕捉动作如何引发物理变化的世界模型，可无需依赖具体具身动作标签即可实现可扩展的机器人学习。像素空间的视频模型提供了广泛的视觉先验，但将模型容量耗费在密集外观重建上，而直接动作模型则需要具身特定标签，阻碍了可扩展性。我们提出$μ_0$——一种基于3D轨迹的可扩展世界模型。与预测密集像素或直接建模动作不同，$μ_0$预测物体、工具、手部和接触区域等显著交互点的平滑3D轨迹，从而生成一种紧凑且与具身无关的运动接口。为了利用多样化视频源进行训练，我们的TraceExtract系统通过选择关键点、构建全局对齐轨迹、以及将运动片段与层次化语言描述关联，自动提取3D监督信号。该TraceExtract监督信号通过结合预训练的视觉-语言骨干网络与模块化轨迹专家（后者利用B样条控制点表示每个查询并预测未来轨迹）对$μ_0$进行预训练。实验表明，$μ_0$在2D和3D轨迹预测上均优于基线方法，包括轨迹预测模型和token化VLM方法。由于$μ_0$被冻结且可重复使用，它可与动作专家配对以支持下游机器人具身。尽管采用无动作预训练，由此产生的轨迹条件策略在性能上可与使用动作监督预训练的VLA模型（如$π_0$）相媲美。这些结果确立了3D轨迹作为一种跨具身操作的可扩展且可迁移的表征形式。