World-4D: 4D Embodied World Models for Robotic Manipulation

Robotic manipulation in the open world requires not only recognizing what a scene looks like, but also anticipating how its 3D structure moves under interaction. We argue that synchronized RGB, depth, and optical flow (RGB-DF) provide a geometry-aware projective representation that makes scene structure and pixel-level motion explicit. Compared to 2D pixel videos, this multi-modal synergy aligns visual appearance with geometric structure and temporal motion, creating a representation space significantly closer to low-level end-effector actions demanded by robotic systems, narrowing the gap between world prediction and policy learning. Building on this insight, we introduce World-4D, a generative model that co-produces future RGB frames, depth maps, and optical flow from a single RGB-D image and a language instruction within one unified diffusion process. This 4D world model features a tri-branch architecture that integrates cross-modal attention with frame-wise 3D RoPE, ensuring that appearance, geometry, and motion evolve consistently. To supply training data at scale, we curate World-4D-200M, a large-scale dataset containing approximately 254 million frames across egocentric human and robotic manipulation videos with pseudo-labels for depth and optical flow. We further propose World-4D-Policy, an inverse dynamics head that consumes the internal 4D representations of World-4D in a single forward pass, bypassing expensive multi-step denoising, to output robot actions in a closed-loop manner. Experiments show that World-4D produces temporally and spatially coherent 4D predictions, and that World-4D-Policy achieves strong performance on real-world bimanual manipulation tasks, outperforming the evaluated baselines on most tasks, with notable gains on tasks demanding spatial precision and temporal coordination.