Local Counterfactual Geometry in World Models: Propose Globally, Correct Locally

A world model can predict how changing an action will change its outcome. We test whether frozen action-conditioned latent predictors get these changes right. We study local counterfactual geometry, the mapping from perturbations around an action plan to predicted future changes conditioned on observation and action history. Comparing predicted and realized effects of the same perturbations tests whether this geometry reflects the environment and where it remains valid. Our experiments show that strong action responses can misrepresent real consequences, and that predicted effects may not transfer across interactions. In control, this source mismatch becomes more consequential as optimization is allowed to move farther from the proposal. The same geometry also supports action refinement: an existing controller supplies a proposal, while the frozen world model computes bounded, goal-directed corrections using the current interaction. We compare released models on the same base action plans and perturbations to measure effect accuracy across perturbation sizes, horizons, and interactions. This offers a complementary view of world-model capability: beyond proposal performance, we ask whether the model can reliably guide local improvement. Local counterfactual geometry thus connects observation and control: propose globally, correct locally.