Identifying Habit, Physics, and Nuisance in Robot World Models

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.

We study action-conditioned world modeling as a scalable way to learn transferable dynamics priors for robot learning. By pretraining a model to predict how actions drive visual scene evolution, the resulting world model captures reusable interaction dynamics beyond appearance-level video generation. Concretely, we pretrain a multi-view interactive base diffusion world model, A2World, on large-scale robot manipulation data with real action annotations. We validate the learned dynamics priors from two complementary perspectives. First, we adapt A2World into a task- or scene-specialized real-world simulator, A2World-sim, whose long-horizon rollouts support simulator-based policy evaluation and scalable what-if analysis by replacing real-robot rollouts with world model rollouts. Second, starting from the same pretrained weights, we adapt A2World into a video-action joint prediction model, A2World-policy, that predicts actions under visual and instruction conditioning. Experiments across simulation benchmarks and real-robot settings demonstrate that action-conditioned world model pretraining yields transferable dynamics priors that benefit both simulator-centric and policy-centric robot learning.

Predicting the next state is a core paradigm of World Models for modeling physical dynamics, emphasizing prediction fidelity. As World Models evolve into World-Action Models (WAMs), existing methods still fix the next state before training as RGB, a single latent feature, or a static combination of predefined targets, thereby constraining action learning to the inductive biases preserved by a particular representation. To address this limitation, we propose CF-WAM, a dynamic next-state prediction framework that samples visual, semantic, geometric, and interaction projections of the same future, standardizes them into a common video form, and supervises a unified WAM across these projections. The action-relevant constraints exposed by these projections accumulate across training steps, forcing WAM to capture the underlying state-transition structure that supports multiple projections of the same action-conditioned future. This dynamic mechanism also provides a natural cross-embodiment dynamics reference frame for Human and Robot learning. By jointly learning across different next-state parameterizations, heterogeneous Human and Robot experience can bypass appearance differences and directly contribute to shared state-transition learning, improving cross-embodiment generalization. Experiments show that CF-WAM improves both training efficiency and final control performance, while translating Human experience effectively into policy gains. CF-WAM achieves state-of-the-art performance on RoboCasa-GR1 with an average success rate of 82.50%, while reaching 82.65% on LIBERO-Plus and up to 84.00% in real-world evaluations.