A Tutorial on World Models and Physical AI

World models, internal simulators that learn the structure and dynamics of an environment, have emerged as a central paradigm in the pursuit of artificial general intelligence, enabling agents to predict, plan, and reason within learned representations. Despite rapid progress across reinforcement learning, robotics, autonomous driving, and video generation, the field lacks a unified framework integrating its diverse architectural choices, training methods, reasoning mechanisms, and application settings. This survey addresses that gap with a multi-axis taxonomy organized along four dimensions: (i) architecture, encompassing representation format, dynamics formulation, input modality, learning paradigm, and downstream application; (ii) methodological family, including state-space and recurrent approaches, transformer-based models, diffusion-based generators, physics-informed networks, and language-augmented multimodal systems; (iii) reasoning strategy, covering imagination-based planning, latent policy learning, counterfactual reasoning, and planning under uncertainty; and (iv) application domain, spanning robotics, autonomous driving, video prediction, multimodal agents, reinforcement learning, scientific modeling, medical imaging, educational measurement, and business and finance. Tracing the field from early cognitive-science foundations to milestone systems such as PlaNet, the Dreamer family, MuZero, Sora, Cosmos, and Genie, we examine how these dimensions interact and highlight the recent convergence of chain-of-thought reasoning with world-model imagination. We review evaluation protocols and benchmarks, identify persistent challenges such as compounding prediction errors, sim-to-real transfer, and fragmented evaluation, and outline future directions toward unified multimodal world models, foundation-scale interactive simulators, and safe deployment in safety-critical domains.

World models -- internal simulators that learn the structure and dynamics of an environment -- have become one of the most actively debated concepts in AI. From model-based reinforcement learning and video generation to embodied robotics and ultimately, physical AI, researchers across AI subfields are building systems that they call "world models", yet there is no consensus on what a world model fundamentally is, what it should predict, or how it should be built. This perspective article provides a scientific definition of world models, discussions of their key technical aspects, and a staged roadmap for developing effective world models.

Embodied AI requires agents that perceive, act, and anticipate how actions reshape future world states. World models serve as internal simulators that capture environment dynamics, enabling forward and counterfactual rollouts to support perception, prediction, and decision making. This survey presents a unified framework for world models in embodied AI. Specifically, we formalize the problem setting and learning objectives, and propose a three-axis taxonomy encompassing: (1) Functionality, Decision-Coupled vs. General-Purpose; (2) Temporal Modeling, Sequential Simulation and Inference vs. Global Difference Prediction; (3) Spatial Representation, Global Latent Vector, Token Feature Sequence, Spatial Latent Grid, and Decomposed Rendering Representation. We systematize data resources and metrics across robotics, autonomous driving, and general video settings, covering pixel prediction quality, state-level understanding, and task performance. Furthermore, we offer a quantitative comparison of state-of-the-art models and distill key open challenges, including the scarcity of unified datasets and the need for evaluation metrics that assess physical consistency over pixel fidelity, the trade-off between model performance and the computational efficiency required for real-time control, and the core modeling difficulty of achieving long-horizon temporal consistency while mitigating error accumulation. Finally, we maintain a curated bibliography at https://github.com/Li-Zn-H/AwesomeWorldModels.