Beyond Thinking: Imagining in 360$^\circ$ for Humanoid Visual Search

Humanoid Visual Search (HVS) requires agents to actively explore immersive 360$^\circ$ environments. While prior methods treat this as a monolithic task relying on cumulative, multi-turn Chain-of-Thought (CoT) reasoning, they impose heavy cognitive burdens and require expensive trajectory-level annotations. In this paper, we propose Imagining in 360$^\circ$, a novel framework that decouples the exploration process into a specialized Imaginator and an Actor. The Imaginator functions as a probabilistic predictor of spatial priors; instead of maintaining a cumulative reasoning chain, it infers the semantic layout of both observed and unobserved regions in a single step. By sampling multiple hypotheses within this semantic space, we provide the Actor with a distribution of effective spatial information, offering robust guidance that hedges against uncertainty during active search. This decoupled architecture significantly lowers data engineering costs by eliminating the need for full-trajectory CoT annotations, enabling the generation of over 1.96 million curated training samples. Extensive experiments demonstrate that explicitly modeling semantic spatial priors drastically improves search efficiency and success rates in complex, in-the-wild environments.