Humanoid robots can acquire complex skills by imitating kinematic humanoid motion references, yet reliable references for contact-rich interactions remain difficult to obtain: motion capture deteriorates under occlusion and close physical contact, while retargeting introduces additional contact and geometric inconsistencies. We present HIGenNTO, a framework that synthesizes humanoid-scene interaction motion references by optimizing the initial noise of a pretrained text-conditioned motion model under sparse spatiotemporal and scene constraints. The same formulation satisfies desired contacts, avoids collisions, and maintains stable support while retaining the prior's realism and temporal coherence, generating interaction motions from scratch and composing long-horizon behaviors stage-wise. Across robot-environment and robot-object tasks, HIGenNTO produces motions that can be executed by tracking policies in simulation and used to train depth-conditioned visuomotor policies operating solely from onboard sensing. We deploy these policies on a Unitree G1 across four contact-rich tasks. Finally, the task specifications themselves can be written by a coding agent, which proposes interaction tasks and compiles them into prompt, constraint, and scene programs, authoring three of our eight evaluated tasks and four further behaviors. Together, these results establish a scalable path from high-level task descriptions to physically executable humanoid interactions.

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