Graph-Operator World Models for Morphology-Parameter Generalization in Continuous Control

World models promise a paradigm shift in robotics, where an agent learns the physics of its environment once and then acquires behaviors efficiently. Yet the learned dynamics models at their core are typically morphology locked. In legged locomotion, a dynamics model trained on an ANYmal-D quadruped fails on a Unitree Go1 because it overfits to one robot's embodiment rather than capturing the locomotion dynamics shared across robots, so even a small change in actuator dynamics or limb length forces retraining from scratch. However, if we formalize a robot's unique physical traits into a morphology specification, a controller for a family of robots can utilize this blueprint in two ways. It can feed the specification to a model-free policy, or it can feed the specification to a learned dynamics model and extract the policy in imagination. We argue for the second route and introduce the Quadrupedal World Model (QWM), which conditions a single generative dynamics model on scale-invariant physical features and trains policies entirely inside it, through a physical morphology encoder, an adaptive reward normalizer, and morphology conditioning in the latent dynamics. Holding the morphology information identical, a model-free policy matches QWM on the training cohort but degrades on unseen morphologies, while QWM transfers zero-shot with no fine-tuning, adaptation, or warm-up in such cases. To our knowledge, this is the first world model to demonstrate zero-shot cross-embodiment transfer within the quadrupedal family.

As one of the mainstream models of artificial intelligence, world models allow agents to learn the representation of the environment for efficient prediction and planning. However, classical world models based on flat tensors face several key problems, including noise sensitivity, error accumulation and weak reasoning. To address these limitations, many recent studies use graph structure to decompose the environment into entity nodes and interactive edges, and model virtual environments in a structured space. This paper systematically formalizes and unifies these emerging graph-based works under the concept of graph world models (GWMs). To the best of our knowledge, GWMs have not yet been explicitly defined and surveyed as a unified research paradigm. Furthermore, we propose a taxonomy based on relational inductive biases (RIB), categorizing GWMs by the specific structural priors they inject: (1) spatial RIB for topological abstraction; (2) physical RIB for dynamic simulation; and (3) logical RIB for causal and semantic reasoning. For each model category, we outline the key design principles, summarize representative models, and conduct comparative analyses. We further discuss open challenges and future directions, including dynamic graph adaptation, probabilistic relational dynamics, multi-granularity inductive biases, and the need for dedicated benchmarks and evaluation metrics for GWMs.

Latent world models are typically trained to predict factual transitions, whereas model predictive control (MPC) must compare alternative actions from the same state. A model can therefore achieve low factual prediction error yet poorly distinguish candidate actions. We introduce AD-WM, an action-discriminative joint-embedding world model for counterfactual MPC. AD-WM combines residual latent dynamics with predictor-level action-recovery regularization, using inverse dynamics and a normalized recovery objective motivated by conditional mutual information. Both objectives encourage planning transitions to preserve action information; their auxiliary heads are discarded at test time, leaving MPC unchanged. On OGBench-Cube, AD-WM improves hard-start success from 3.7% to 52.0% over a matched LeWM baseline and improves mean success over the reproduced baseline in four of five simulation environments. Planning diagnostics show that factual prediction error and whole-bank action ranking do not follow the closed-loop success ordering, whereas CEM-aligned elite regret tracks success more closely. With a frozen V-JEPA 2 encoder and matched DROID post-training, AD-WM also improves zero-shot transfer to our Franka setup, increasing basic pick-and-place success from 42.2% to 71.1% without lab-specific adaptation. These results suggest that world models for planning should preserve action-dependent differences needed for counterfactual selection, rather than optimize factual prediction accuracy alone. More videos and code are available at https://ad-wm.github.io/.