Learning Transferable Dynamics Priors from Action to World Modeling

World models are increasingly used in embodied intelligence and generative simulation, yet their scope remains ambiguous across communities. This tutorial presents a design-space view of world models as action-conditioned predictive models that estimate the future evolution of task-relevant observations or states. We categorize existing methods into observation-space and state-space world models, comparing their trade-offs in visual fidelity, spatial structure, physical interpretability, and control usability. We further introduce world action models, which connect predicted futures with executable robot actions, and summarize four representative paradigms: imagine-then-execute, video-feature-conditioned action prediction, joint video-action modeling, and auxiliary video prediction for policy learning. The goal of this tutorial is to clarify the conceptual scope of world (action) models and provide a structured taxonomy for embodied prediction and control.

Bridging the sim-to-real gap is a core challenge in deploying learned manipulation policies. Sim-to-real learning is attractive because it can replace expensive real robot demonstrations with scalable synthetic data, yet world-action models have not previously been shown to transfer from simulation to real robotic manipulation. We study whether a world-action model can be trained from synthetic priors and deployed zero-shot in the real world. To this end, we build upon Cosmos Policy, a video diffusion model adapted for visuomotor control. We construct simulation environments with extensive domain randomization and generate demonstrations using the AnyTask motion planning pipeline. We evaluate our approach across object lifting, drawer opening, and pick-and-place tasks using ${\sim}800$ synthetic demonstrations per task and no real demonstrations. When deployed zero-shot on a Franka Robot, our policy attains a 35% average success rate. To our knowledge, this represents the first successful sim-to-real transfer of a world-action model for robotic manipulation.

World models, which are predictive representations of how environments evolve under actions, have become a central component of robot learning. They support policy learning, planning, simulation, evaluation, data generation, and have advanced rapidly with the rise of foundation models and large-scale video generation. However, the literature remains fragmented across architectures, functional roles, and embodied application domains. To address this gap, we present a comprehensive review of world models from a robot-learning perspective. We examine how world models are coupled with robot policies, how they serve as learned simulators for reinforcement learning and evaluation, and how robotic video world models have progressed from imagination-based generation to controllable, structured, and foundation-scale formulations. We further connect these ideas to navigation and autonomous driving, and summarize representative datasets, benchmarks, and evaluation protocols. Overall, this survey systematically reviews the rapidly growing literature on world models for robot learning, clarifies key paradigms and applications, and highlights major challenges and future directions for predictive modeling in embodied agents. To facilitate continued access to newly emerging works, benchmarks, and resources, we will maintain and regularly update the accompanying GitHub repository alongside this survey.