Latent State Design for World Models under Sufficiency Constraints

A latent world model may achieve accurate short-horizon prediction while still inducing a latent space that is poorly aligned with planning. A key issue is spatiotemporal mismatch: these models are often trained with local predictive supervision, but deployed for long-horizon goal-directed search in latent spaces where Euclidean distance may not reflect what is reachable within a finite action budget. We present the Reachability-Correction auxiliary objective (RC-aux), a lightweight correction for this mismatch in reconstruction-free latent world models. RC-aux keeps the world-model backbone unchanged and adds planning-aligned supervision along two axes. Along the time axis, multi-horizon open-loop prediction trains the model beyond one-step consistency. Along the space axis, budget-conditioned reachability supervision, together with temporal hard negatives, encourages the latent space to distinguish states that are eventually reachable from those reachable within the current planning horizon. At test time, the learned reachability signal can also be used by a reachability-aware planner to favor trajectories that are both goal-directed and attainable under the available budget. We instantiate RC-aux on LeWorldModel and evaluate it under both continuation-training and matched-from-scratch settings. Across goal-conditioned pixel-control tasks and a LIBERO-Goal extension, RC-aux improves LeWM-style planning with modest additional cost. These results suggest that planning with latent world models depends not only on predictive accuracy, but also on whether the learned representation encodes the temporal and geometric structure required by downstream search. The code is available at https://github.com/Guang000/RC-aux.

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.

Learning and planning in imagination using world models provides an effective paradigm for training agents for decision-making. However, existing approaches often rely on high-dimensional latent spaces or generic visual embeddings that retain many factors irrelevant to control, limiting efficiency and generalization across tasks. To this end, we study how agents can learn world models with representations that are task-specific, minimal, and sufficient for decision-making. We achieve this via a closed-loop synergy between the agent and the world model, in which structured world-model learning distills task-sufficient representations from informative interaction data. On the agent side, agents actively probe the environment to collect informative trajectories that expose task-relevant latent factors, guided by an adaptive curriculum. On the world-model side, we learn structured representations over observations to distill compact, task-sufficient latent states from the collected interaction data. This synergy enables the empirical recovery of task-sufficient latent representations that capture all control-relevant factors. Leveraging these representations, the resulting policies achieve improved sample efficiency and generalization, including generalization across skills, object-skill compositions, and previously unseen tasks on standard continuous-control and robotic-manipulation benchmarks.