What if a video generation model could not only imagine a plausible future, but the correct one, accurately reflecting how the world changes with each action? We address this question by presenting the Egocentric World Model (EgoWM), a simple, architecture-agnostic method that transforms any pretrained video diffusion model into an action-conditioned world model, enabling controllable future prediction. Rather than training from scratch, we repurpose the rich world priors of Internet-scale video models and inject motor commands through lightweight conditioning layers. This allows the model to follow actions faithfully while preserving realism and strong generalization. Our approach scales naturally across embodiments and action spaces, ranging from 3-DoF mobile robots to 25-DoF humanoids, where predicting egocentric joint-angle-driven dynamics is substantially more challenging. The model produces coherent rollouts for both navigation and manipulation tasks, requiring only modest fine-tuning. To evaluate physical correctness independently of visual appearance, we introduce the Structural Consistency Score (SCS), which measures whether stable scene elements evolve consistently with the provided actions. EgoWM improves SCS by up to 80 percent over prior state-of-the-art navigation world models, while achieving up to six times lower inference latency and robust generalization to unseen environments, including navigation inside paintings.