Enabling humanoid robots to exploit physical contact, rather than simply avoid collisions, is crucial for autonomy in unstructured environments. Traditional optimization-based planners struggle with contact complexity, while on-policy reinforcement learning (RL) is sample-inefficient and has limited multi-task ability. We propose a framework combining a learned world model with sampling-based Model Predictive Control (MPC), trained on a demonstration-free offline dataset to predict future outcomes in a compressed latent space. To address sparse contact rewards and sensor noise, the MPC uses a learned surrogate value function for dense, robust planning. Our single, scalable model supports contact-aware tasks, including wall support after perturbation, blocking incoming objects, and traversing height-limited arches, with improved data efficiency and multi-task capability over on-policy RL. Deployed on a physical humanoid, our system achieves robust, real-time contact planning from proprioception and ego-centric depth images. Website:this https URL
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