Seeing and Imagining as One: Unified Video Generation and 4D Perception for Embodied World Modeling

Embodied agents require robust and comprehensive 3D spatiotemporal representations to support spatial reasoning, manipulation understanding, and downstream decision making. However, existing robot data are typically captured from fixed or sparse viewpoints, providing only partial and view-dependent observations, which limits multi-view perception and generalization across viewpoints. Given the difficulty of collecting additional viewpoints in real-world settings, we propose Embody4D, a dedicated video-to-video world model for embodied scenarios to bridge this observation gap by transforming a monocular robot video into novel-view videos from flexible target camera viewpoints. First, to tackle training data scarcity, we introduce a 3D-aware compositional synthesis pipeline to curate a heterogeneous dataset compositing cross-embodiment robotic arms with diverse backgrounds, promoting broad generalization. Second, to enforce geometric stability, we devise a latent confidence-aware expert modulation strategy, which estimates the reliability of warped latent priors and adaptively routes regions to copy, repair, or inpaint experts for spatiotemporally consistent 4D generation. Finally, to enhance the fidelity of the manipulation, we incorporate an interaction-aware attention mechanism that explicitly attends to the robotic interaction regions. Extensive experiments show that Embody4D achieves state-of-the-art performance on visual evaluation benchmarks, while both simulated and real-world robotic experiments further demonstrate its effectiveness as a robust data engine for synthesizing high-fidelity, view-consistent videos that empower downstream robotic planning and learning.

Video world models can generate realistic futures from a single instruction, but they often fail to track the same physical points consistently across 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 both simulation and realistic scenarios and improves real-world manipulation success from 61% to 81%. Additional results are available at https://gem-4d.github.io/.

World-model-based imagine-then-act becomes a promising paradigm for robotic manipulation, yet existing approaches typically support either purely image-based forecasting or reasoning over partial 3D geometry, limiting their ability to predict complete 4D scene dynamics. This work proposes a novel embodied 4D world model that enables geometrically consistent, arbitrary-view RGBD generation: given only a single-view RGBD observation as input, the model imagines the remaining viewpoints, which can then be back-projected and fused to assemble a more complete 3D structure across time. To efficiently learn the multi-view, cross-modality generation, we explicitly design cross-view and cross-modality feature fusion that jointly encourage consistency between RGB and depth and enforce geometric alignment across views. Beyond prediction, converting generated futures into actions is often handled by inverse dynamics, which is ill-posed because multiple actions can explain the same transition. We address this with a test-time action optimization strategy that backpropagates through the generative model to infer a trajectory-level latent best matching the predicted future, and a residual inverse dynamics model that turns this trajectory prior into accurate executable actions. Experiments on three datasets demonstrate strong performance on both 4D scene generation and downstream manipulation, and ablations provide practical insights into the key design choices.