BFMT: Enhancing Search Capabilities of Tree Sampler via Bootstrap Flow-Map Tree

The ability to efficiently navigate high-dimensional spaces to identify optimal candidates-whether designing targeted molecular structures or generating images with preferred attributes-stands as a central pillar of modern scientific progress. Recent tree-based samplers enable highly scalable inference-time search by eliminating the reward-gradient bottleneck inherent to particle-based methods. Despite their potential, existing tree-based samplers are fundamentally constrained by the massive number of function evaluations (NFEs) required for node valuation, crippling their utility in exploration-heavy tasks. Furthermore, their reliance on small, uniform transitions at each depth precludes dynamic, adaptive search capabilities. To address this, we introduce Bootstrap Flow-Map-Tree (a.k.a BFMT), a computationally efficient sampling framework that enables full tree-path construction from any tree depth using a single function evaluation, drastically reducing computational overhead while providing critical foresight for sequential sampling. By enabling dynamic transition time-step scheduling, BFMT efficiently allocates its sampling budget, smoothly transitioning from broad global exploration to fine-grained local refinement of high-utility modes discovered through exploration. Extensive experiments and ablation studies across diverse domains-from high-dimensional images to large-scale molecules-demonstrate BFMT's superiority over baseline approaches in both search and alignment tasks.