Humanoid locomotion across complex terrain demands forward-looking exteroception to anticipate obstacles, yet this signal is unreliable in real-world deployment, failing partially and intermittently. Existing perceptive policies often assume that depth observations remain clean and in-distribution, while recent attempts to unify perceptive and blind control typically route or switch between separate sub-policies, leaving recoverable information in partially corrupted depth unexploited. We instead propose CAP, a single-stage humanoid locomotion policy that recovers this signal with a perceptive world-model encoder trained as a learned denoiser to reconstruct clean depth from a corrupted input, together with a co-active proprioceptive variational encoder that supplies depth-free body-state information. A coupled training recipe pairs a depth-noise curriculum on the world-model input with world-model feature dropout on the policy-facing latent, exposing the policy to failures across the entire perception-quality spectrum. In simulation, CAP matches or improves upon perceptive baselines when depth remains informative, and degrades more smoothly than a binary-switching baseline as perception worsens. On the Unitree G1, controlled trials and indoor-outdoor deployments demonstrate perception-robust locomotion under intermittent occlusion, real-sensor corruption, and outdoor depth artifacts.