Monolithic world models predict the entire next state at every step, spending capacity re-predicting the static majority of a scene and injecting error into it. We ask whether explicitly modeling change (a per-object change gate plus a residual delta head that perturbs only the objects the gate flags) is a more effective and interpretable bias for physical prediction and control. On a MuJoCo tabletop pushing benchmark scaling from 3 to 8 objects, the sparse/residual model predicts next-state poses 2.5 to 4.6 times more accurately than a dense multilayer perceptron at 8.6 to 11.1 times fewer parameters, sustains change-detection F1 of 0.80 to 0.87 where the dense baseline is degenerate, transfers across object counts with zero retraining (99.4 percent F1 retention), and reaches about 90 percent of its full-data accuracy with a quarter of the data. In autoregressive rollout it compounds far less error, hugging the no-motion floor while the dense model drifts. Finally, inside a sampling-based planner, prediction-only models fail (though a true-simulator oracle solves the task with the identical planner, confirming the planner is sound), but once featurized and trained for the states a planner visits, the sparse model begins to plan (0.23 plus or minus 0.06 success over three seeds) while the dense monolith stays at zero at every seed. Modeling what changes, rather than re-predicting the whole world, is a simple, effective bias for object-centric physical AI; code, data generators, and all checkpoints will be released upon publication.
A central challenge in visual intelligence is learning the physical structure of scenes from raw videos: how regions form objects and the laws that govern their interactions. Solving these tasks requires world models capable of inferring distributional states of the world from partial observations - capabilities that current architectures do not provide. We introduce a new class of probabilistic world models that support estimation of the probability of any visual variable, such as appearance and dynamics, conditioned on any other variables. Here, we identify that these models can be trained efficiently with autoregressive sequence modeling, yielding world models from which rich object understanding emerges. First, we demonstrate that our model captures the physical laws governing how objects move by generating multiple plausible future states of the world through sequential inference. Then, by analyzing motion correlations across these futures, we extract objects and articulated object subparts. Having discovered these objects, we show that our world model can manipulate them in 3D. Finally, we demonstrate how physical relationships between objects can be computed from the world model, enabling applications such as Visual Jenga.
Predicting how deformable objects evolve under robotic manipulation is a longstanding challenge. Existing approaches typically rely on per-object optimization to fit material parameters, which can be slow and cannot generalize, while end-to-end learned alternatives extrapolate poorly and often violate basic physical structure. We present PhysCoRe, a physics-corrected residual world model that couples a differentiable Material Point Method (MPM) simulator with two feed-forward neural networks. A material refinement module, Material from Motion (MfM), infers per-particle elasticity from visual observations, grounding the simulator in object-specific physics. A residual correction module, Residual from Dynamics (RfD), learns the discrepancy and predicts corrections to the simulator's internal dynamics, absorbing systematic biases that the analytical model cannot capture. This design also supports online material identification on novel objects. MfM adapts from limited interactions, and its predictive uncertainty steers further exploration toward the regions where its estimate is least confident. Experiments on real deformable-object manipulation sequences show that PhysCoRe outperforms state-of-the-art baselines in prediction accuracy, and that its predicted confidence forms a reliable distribution across the object's geometry, providing a natural signal for future confidence-guided exploration.
World modeling is emerging as a central principle for building intelligent systems capable of prediction, reasoning, and decision making. A central distinction can be drawn between explicit world models, which learn structured dynamics for rollout-based reasoning and planning, and implicit world models, which encode predictive structure within scalable learned representations. These complementary paradigms provide a foundation for physical AI in domains such as robotics and autonomous driving, enabling intelligence beyond reactive control under real-world constraints. Recent foundation models further suggest a pathway toward unified systems integrating perception, prediction, and action. Despite rapid progress, major challenges remain in hierarchical reasoning, long-horizon planning, and autonomous goal formation, which are critical for advancing toward artificial general intelligence. This tutorial presents a coherent framework in which diverse world modeling approaches are unified through shared predictive structure and differentiated by how such structure is represented and exploited.