LATS: Levy Adaptive Tree Sampling for Feedback-Driven Diverse Target Discovery

While diffusion models excel at capturing complex data distributions, scientific discovery often requires steering generation toward specific, uncharacterized regions that maximize a target objective. These high-utility modes frequently reside in low-likelihood tail regions and are only revealed sequentially through interactive feedback. Existing diffusion samplers fail in this regime: they inherit the pre-trained model's bias toward high-density regions, leaving rare yet promising phenomena underexplored. Conversely, exploration-heavy samplers ensure broad coverage but fail to efficiently exploit high-utility modes when constrained by a strict sampling budget. To resolve this dilemma, we introduce Levy Adaptive Tree Search (LATS), a principled sampling framework for online feedback-driven search. LATS leverages heavy-tailed exploration coupled with tree-based value backpropagation to progressively uncover preferred modes. By maintaining broad distributional coverage, LATS successfully discovers low-likelihood, high-utility regions while preserving sample fidelity and structural diversity. Experiments across diverse benchmarks, including materials science, demonstrate that LATS significantly outperforms baselines in target discovery efficiency.