Understanding 3D scenes requires flexible combinations of visual reasoning tasks, including depth estimation, novel view synthesis, and object manipulation, all of which are essential for perception and interaction. Existing approaches have typically addressed these tasks in isolation, preventing them from sharing a common representation or transferring knowledge across tasks. A conceptually simpler but practically non-trivial alternative is to unify these diverse tasks into a single model, reducing different tasks from separate training objectives to merely different prompts and allowing for joint training across all datasets. In this work, we present a physical world model for unified 3D understanding and interaction (3WM), formulated as a probabilistic graphical model in which nodes represent multimodal scene elements such as RGB, optical flow, and camera pose. Diverse tasks emerge from different inference pathways through the graph: novel view synthesis from RGB and dense flow prompts, object manipulation from RGB and sparse flow prompts, and depth estimation from RGB and camera conditioning, all zero-shot without task-specific training. 3WM outperforms specialized baselines without the need for finetuning by offering precise controllability, strong geometric consistency, and robustness in real-world scenarios, achieving state-of-the-art performance on NVS and 3D object manipulation. Beyond predefined tasks, the model supports composable inference pathways, such as moving objects aside while navigating a 3D environment, enabling complex geometric reasoning. This demonstrates that a unified model can serve as a practical alternative to fragmented task-specific systems, taking a step towards a general-purpose visual world model.