Predictive world models provide compact visual representations for control.
Control requires a latent geometry aligned with temporal reachability rather than predictive similarity alone.
We introduce Directed Temporal Representations for Control (DTRC)
DTRC learns such a geometry from offline visual trajectories on top of frozen LeWorldModel (LeWM) features.
DTRC constructs a directed temporal quasimetric over the learned control representation.
Short-range temporal offsets calibrate the distance scale.
Bootstrapped targets extend temporal reachability across longer horizons.
Action-conditioned consistency aligns the representation with local transition dynamics.
The resulting distance estimates temporal reaching cost, and its change across a transition defines goal-relative temporal progress.
We use this progress signal as a temporal critic for direct goal-conditioned policy learning.
Model-assisted targets provide an additional training-time refinement under behavior-support and dynamics-agreement constraints.
Performance across ten visual control tasks
DTRC achieves strong goal-conditioned control performance relative to planning and direct-policy baselines.
Held-out diagnostics on the four LeWM tasks
Consistent short-range temporal calibration, task-dependent long-range and directional structure, and positive transition-level progress.
Temporal supervision improves the same flow-policy parameterization across all four LeWM tasks
While the resulting policy acts directly without iterative trajectory search at test time.