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

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.

Tree-based samplers offer a compelling alternative for scalable inference-time search, bypassing the per-step reward and gradient dependencies that introduce systematic bias into SMC-style frameworks. Despite this advantage, contemporary tree samplers fail to achieve broad exploration. Their reliance on learned, DDPM-like transitions inherently couples neighbor states in a trajectory, thereby restricting child-parent feature divergence in the tree sampler. Consequently, these samplers suffer from restricted coverage of the target marginal distribution, severely hindering the exploration critical for efficient search under sparse reward. To overcome these limitations, we introduce a simple yet effective Bootstrap Stochastic Interpolant Tree (BSIT) sampler that decouples child node generation from explicit parent dependencies. By expanding the degrees of freedom during child node sampling, BSIT encourages diverse trajectory rollouts and unlocks broader path-space diversity-the exact catalyst needed for efficient exploration. Crucially, we show that BSIT's improved exploration accelerates convergence to the target distribution while achieving broader distributional coverage than samplers that rely on DDPM-like transitions for child-node generation, all without incurring additional function evaluations or reward feedback, thereby providing a highly efficient basis for rare target search. Extensive experiments across diverse search settings, including rare-species discovery and target-aligned molecule generation tasks, demonstrate BSIT's superior search efficiency over the baselines.

Amortized inference is the task of training a parametric model, such as a neural network, to approximate a distribution with a given unnormalized density where exact sampling is intractable. When sampling is implemented as a sequential decision-making process, reinforcement learning (RL) methods, such as generative flow networks, can be used to train the sampling policy. Off-policy RL training facilitates the discovery of diverse, high-reward candidates, but existing methods still face challenges in efficient exploration. We propose to use an adaptive training distribution (the \teacher) to guide the training of the primary amortized sampler (the \student). The \teacher, an auxiliary behavior model, is trained to sample high-loss regions of the \student and can generalize across unexplored modes, thereby enhancing mode coverage by providing an efficient training curriculum. We validate the effectiveness of this approach in a synthetic environment designed to present an exploration challenge, two diffusion-based sampling tasks, and four biochemical discovery tasks demonstrating its ability to improve sample efficiency and mode coverage. Source code is available at https://github.com/alstn12088/adaptive-teacher.