Video world models can generate realistic futures from a single instruction, but they often fail to preserve consistent point-level motion over time. As a result, the generated videos appear plausible, yet lack the physical grounding required for reliable action execution, such as robot manipulation. We present GEM-4D, a geometry-grounded video world model that resolves this limitation by injecting dense 4D correspondence supervision, distilled from a pretrained geometry foundation model, into the video generative backbone during training. This supervision enables the model to jointly capture appearance and geometric structure while retaining a single-stream architecture with no additional inference cost. We further introduce an inverse dynamics module that converts correspondence-consistent video rollouts into executable robot trajectories, enabling direct deployment in both real-world and simulated manipulation. GEM-4D achieves state-of-the-art performance on both video prediction and geometric consistency across simulation and realistic scenarios and improves real-world manipulation success from 61% to 81%. Additional results are available at the project page: https://anonymous-submission-20.github.io/gem.github.io/.
@article{arxiv.2605.22882,
title = {GEM-4D: Geometry-Enhanced Video World Models for Robot Manipulation},
author = {Kaichen Zhou and Yuzhen Chen and Fangneng Zhan and Hang Hua and Grace Chen and Xinhai Chang and Ao Qu and Yilun Du and Zhuang Liu and Paul Pu Liang and Mengyu Wang},
journal= {arXiv preprint arXiv:2605.22882},
year = {2026}
}