Learning Action-Conditional and Object-Centric Gaussian Splatting World Models for Rigid Objects

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.

Vision-language-action (VLA) policies have advanced language-conditioned robotic manipulation by transferring semantic priors from pretrained vision-language models to action generation. However, standard action-imitation learning often lacks sufficient modeling of explicit 3D spatial information, dense geometric supervision, and future environment evolution, all critical for precise robotic interaction. To address this, we propose \textbf{GaussianDream}, a feed-forward 3D Gaussian world-model plug-in. Specifically, we introduce learnable GaussianDream Queries in the encoder, enabling the model to capture current-frame 3D spatial structure and short-horizon future evolution. During training, the latent GaussianDream prefix is processed by a static reconstruction head and a future prediction head to produce current 3D Gaussian scene states and future Gaussian evolution states. The current branch is supervised by RGB rendering and depth, while the future branch uses future RGB, depth, and pseudo 3D scene-flow signals. During inference, GaussianDream discards all auxiliary heads and retains only the learned prefix to condition action generation, without test-time Gaussian reconstruction or future prediction. Experimental results demonstrate that GaussianDream achieves state-of-the-art performance across multiple robotic manipulation benchmarks, reaching \textbf{98.4%} on LIBERO, \textbf{54.8%} on RoboCasa Human-50, and \textbf{50.0%} on real-robot tasks. Compared with existing 3D-enhanced VLA methods, GaussianDream achieves strong accuracy while providing higher inference efficiency than video-based world-model approaches.

Robotic manipulation depends on the ability to anticipate how actions reshape objects, contacts, and scene geometry before execution. Learned world models provide this capability by predicting task-relevant future evolution under robot intervention, yet the term now spans latent dynamics models, action-conditioned video generators, three- and four-dimensional scene predictors, physics-informed simulators, and predictive modules inside vision-language-action systems. This breadth has fragmented the literature and obscured the design choices that matter for manipulation. We survey world models for robotic manipulation through three questions: what future representation is predicted, how prediction is connected to action, and when prediction is used in the robot-learning pipeline. We operationally define a world model as an action-conditioned predictive system and distinguish it from perception modules, inverse models, policies, rewards, and value functions. We then organize existing work into five representation families, develop a functional taxonomy that separates integrated prediction-action models from explicit predictive planners, and characterize infrastructure roles including synthetic experience generation, candidate filtering, search-based evaluation, learned environments, and outcome verification. We further map these roles across pretraining, post-training, and inference adaptation, review 34 manipulation datasets, and synthesize evaluation protocols for predictive fidelity, task performance, and simulator reliability. This survey shows that world models are evolving from task-specific dynamics predictors into predictive infrastructure for robot learning, while exposing open challenges in contact modeling, hallucination control, action alignment, and benchmarking under closed-loop use.