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.
Figures & tables
Figure 1: Unlike SMC (which suffers from noisy reward gradient guidance) and DTS (which is constrained by Gaussian bias), LATS discovers high-utility tail modes (Viz., using MNIST digits 7 and 9 as targets, which are the two least represented categories during training) while avoiding off-manifold sample generation. LATS leverages online feedback to enrich intra-target class diversity actively, thereby avoiding mode collapse.
Figure 2: Overview of the Lévy Adaptive Tree Search (LATS) Framework. (Stage 1) The generative model uses heavy-tailed Lévy noise rather than Gaussian noise, extending structural coverage to the data manifold’s rare long-tail modes. (Stage 2) LATS constructs a dynamic search tree built upon the trained Lévy transition dynamics to systematically explore the latent space. (Stage 3) Guided by feedback, a soft Bellman value backup mechanism propagates reward signals upward, allowing the SelectUCT score to aggressively prune low-value paths while continuously amplifying the discovery of high-utility targets without fine-tuning the Lévy model.
Target
Method
MNIST-LT
CIFAR-10-LT
ImageNet-LT
FID ↓
MMD ↓
QADAS ↑
FID ↓
MMD ↓
QADAS ↑
FID ↓
MMD ↓
QADAS ↑
Set 1
SMC
1.8137
13.748
11.8700
3.7810
3.8231
9.9300
2.1463
2.8476
12.9748
DTS
1.2532
9.4025
14.8631
0.9021
3.1071
13.0262
0.9444
1.7802
18.8476
FKS
1.0699
7.5111
14.0710
0.8150
2.4711
11.4592
1.4609
2.0285
17.4755
LATS
0.7264
5.5532
18.7452
0.7223
1.7286
14.0967
0.7588
0.7692
20.1346
Set 2
SMC
4.0168
18.9856
6.7324
3.7970
6.8242
0.0000
3.4637
6.7032
5.2677
Table 1: Quantitative Comparison with B=250 . We report FID (lower is better), MMD (lower is better), and the QADAS diversity metric (higher is better) across two distinct target sets for each dataset. LATS consistently outperforms baselines in maintaining sample quality while uncovering diverse target modes.
Method
MICRO2D ( B=250 )
FID ↓
MMD ↓
QADAS ↑
SMC
4.2154
29.8165
0.0000
DTS
2.8699
17.7681
4.6196
FKS
3.5499
27.7336
0.0000
LATS
0.9464
4.2721
6.1041
Table 2: MICRO2D for Set S2.
Figure 3: Qualitative comparison of generation diversity and quality across target sets and datasets. While DTS and FKS tend to focus on dominant modes, LATS uncovers diverse, high-utility samples by leveraging Lévy-driven exploration and tree-based online value backup, aiding history-aware exploitation while maintaining sample quality. long-tail high-utility classes are denoted as blue .
Figure 4: Quantitative Comparisons across Sampling Budgets. Comparison of LATS against baselines across MNIST-LT, CIFAR-10-LT, and ImageNet-LT for target Set S2. LATS achieves the fastest convergence in quality and target discovery while maintaining significantly higher sample diversity as the sampling budget increases.
Appendix figures & tables4 assets
Supplementary material from the paper’s appendix.
Appendix
Method
CIFAR-10-LT
ImageNet-LT
FID ↓
MMD ↓
QADAS ↑
FID ↓
MMD ↓
QADAS ↑
LATS w β = 0
0.8657
2.2700
12.6108
0.8976
0.8637
18.7534
LATS w β = 0.1
0.8264
2.0361
13.3479
0.7846
0.8211
18.9304
LATS w β = 1
0.7223
1.7286
14.0967
0.7588
0.7692
20.1346
Appendix
Table 3: Analysis of Different Exploration Factor β . We evaluate performance under different Exploration factor β with a sampling budget of 250 . For this study, the target sets on each dataset include a mix of frequent and rare classes (i.e., Set S1 ).
Method
CIFAR-10-LT
ImageNet-LT
FID ↓
MMD ↓
QADAS ↑
FID ↓
MMD ↓
QADAS ↑
LATS w/o Exploration term in node selection mechanism
0.8657
2.2700
12.6108
0.8976
0.8637
18.7534
LATS w/o Online Value Backup
1.0877
4.0201
6.8011
1.6677
6.1229
8.5721
LATS
0.7223
1.7286
14.0967
0.7588
0.7692
20.1346
Appendix
Table 4: Analysis of Different Components of LATS. We evaluate performance under a sampling budget of 1000. For this study, the target sets on each dataset include a mix of frequent and rare classes (i.e., Set S1 ).
Figure 5: Qualitative comparison of generation diversity and quality across target sets and datasets (MNIST-LT, ImageNet-LT examples). We compare LATS against the DTS, FKS baseline on MNIST-LT and ImageNet-LT on representative target sets.
Figure 6: Qualitative comparison of generation diversity and quality across target sets and datasets (ImageNet-LT examples). We compare LATS against the DTS, FKS baseline on ImageNet-LT on representative target sets.
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.
Binglin Ji, Anindya Sarkar, Hengchang Lu +4
Department of CSE, Washington University in St.Louis, USA · Department of Information Technology, Uppsala University, Sweden
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.
Binglin Ji, Anindya Sarkar, Yevgeniy Vorobeychik
Department of Computer Science & Engineering, Washington University in St. Louis, USA
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.