For perceptive humanoid locomotion, the relevance of terrain geometry depends on the robot's body state and how both evolve under its actions. Existing work has advanced terrain-aware sensory fusion and cross-modal prediction, improving how visual and proprioceptive information is combined and related. However, feature aggregation alone does not specify which cross-modal relationships should be learned, while prediction between simultaneous observations does not explicitly constrain their action-dependent evolution. We present Spatiotemporal Training with Explicit Prediction (STEP), a one-stage framework that jointly supervises cross-modal relationships and action-dependent state evolution within a shared control representation. Multiple learned queries aggregate depth and proprioceptive tokens into a compact policy state. Bidirectional masked prediction uses each visible modality to predict latent features of the omitted modality, explicitly supervising terrain-body relationships. An action-conditioned predictor maps the current policy state and executed action to the next fused state, with an exponential-moving-average target defined directly in the policy representation space. Simulation comparisons show overall improvements in terrain traversal over evaluated fusion alternatives and ablations, while depth-dropout and delay experiments demonstrate the benefits of both predictive objectives under degraded visual input. Deployed on a 23-DoF Noetix E1 humanoid with onboard sensing, STEP succeeds in 98 of 100 hardware trials across stairs, a 40\,cm platform, a 70\,cm gap, stepping stones, and backward stair traversal without rearward terrain visibility.
We present a progressive imitation framework that learns terrain-appropriate humanoid parkour skills and subsequently adapts their hand--knee support. Human demonstrations provide traversal behaviors, but their contact patterns need not suit a robot's proportions or the available support surfaces. Our framework changes the role of demonstrations across three stages: privileged imitation produces physically executable robot references; terrain-indexed adversarial motion priors guide skill acquisition; and geometric support guidance with a reduced motion-prior weight enables contact adaptation. Candidate-based precontact attraction and actual-contact evaluation guide support without prescribing a contact sequence. The deployed policy selects behaviors from onboard depth, proprioception, and velocity commands without an external skill label. On the Noetix E1, the policy achieves 96.34\% hybrid success in simulation and transfers without real-world policy fine-tuning, completing 29 of 30 individual obstacle trials and four of five hybrid courses. Support-adaptation ablations show higher traversal success for the complete adaptation stage on the tested terrains, while qualitative observations show changes in contact placement. These results support acquiring skills from demonstrations before relaxing their influence to accommodate robot-specific support configurations.