TIDE: The Reachability–Learnability Gap in Temporal Intent Control

Visual world models support goal-directed control through learned latent representations used for direct execution or decision-time search, yet search may succeed when direct execution fails. This discrepancy raises three questions: What behaviors can a frozen system execute? Which can finite-budget search discover? And which can a shared model recover without online search? Focusing on goal-conditioned visual control with frozen, action-conditioned jointembedding predictive world models, we introduce TIDE, a controlled empirical framework that equips each frozen representation with a standardized intentconditioned execution head and varies only the temporal structure of bounded intent corrections. Specifically, we compare SINGLE one-shot corrections, SHARED corrections reused across execution calls, and DYNAMIC call-specific corrections to study how temporal intervention structure affects reachability, searchability, and learnability. In a matched intervention evaluation based on Push-T, DYNAMIC call-specific corrections uncover more validated successful behaviors. Across four control tasks (Push-T, Cube, Reacher, and TwoRoom) and two frozen backbones (LeWM and Fast-LeWM), persistent SHARED corrections are more consistently effective under matched finite search budgets. Validated SHARED interventions can also be partially amortized into search-free control, although the gains remain modest and offline learning signals alone do not reliably predict closed-loop improvement. These findings expose a control-interface gap in this class of frozen visual world models: predictive latent representations do not by themselves ensure that reachable behavior is readily searchable or learnable.