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

arXiv: https://arxiv.org/abs/2607.02915 · HTML: https://mlsanity.com/paper/2607.02915/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 33 references that are in the map.
- First posted on arXiv 3 Jul 2026.

## Builds on (most cited first, 26 of 26)

- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Grounding DINO: Marrying DINO with Grounded Pre-Training for Open-Set Object Detection](https://mlsanity.com/paper/2303.05499/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Evaluating Text-to-Visual Generation with Image-to-Text Generation](https://mlsanity.com/paper/2404.01291/) (2024)
- [T2I-CompBench++: An Enhanced and Comprehensive Benchmark for Compositional Text-to-image Generation](https://mlsanity.com/paper/2307.06350/) (2023)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [A General Framework for Inference-time Scaling and Steering of Diffusion Models](https://mlsanity.com/paper/2501.06848/) (2025)
- [Theoretical guarantees on the best-of-n alignment policy](https://mlsanity.com/paper/2401.01879/) (2024)
- [How to build a consistency model: Learning flow maps via self-distillation](https://mlsanity.com/paper/2505.18825/) (2025)
- [Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts](https://mlsanity.com/paper/2503.02819/) (2025)
- [Test-time Alignment of Diffusion Models without Reward Over-optimization](https://mlsanity.com/paper/2501.05803/) (2025)
- [Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Review](https://mlsanity.com/paper/2501.09685/) (2025)
- [SANA-Sprint: One-Step Diffusion with Continuous-Time Consistency Distillation](https://mlsanity.com/paper/2503.09641/) (2025)
- [GenAI Arena: An Open Evaluation Platform for Generative Models](https://mlsanity.com/paper/2406.04485/) (2024)
- [Feedback Efficient Online Fine-Tuning of Diffusion Models](https://mlsanity.com/paper/2402.16359/) (2024)
- [Categorical Flow Maps](https://mlsanity.com/paper/2602.12233/) (2026)
- [Dynamic Search for Inference-Time Alignment in Diffusion Models](https://mlsanity.com/paper/2503.02039/) (2025)
- [Meta Flow Maps enable scalable reward alignment](https://mlsanity.com/paper/2601.14430/) (2026)
- [Diffusion Tree Sampling: Scalable inference-time alignment of diffusion models](https://mlsanity.com/paper/2506.20701/) (2025)
- [Debiasing Guidance for Discrete Diffusion with Sequential Monte Carlo](https://mlsanity.com/paper/2502.06079/) (2025)
- [Diamond Maps: Efficient Reward Alignment via Stochastic Flow Maps](https://mlsanity.com/paper/2602.05993/) (2026)
- [Training-Free Guidance Beyond Differentiability: Scalable Path Steering with Tree Search in Diffusion and Flow Models](https://mlsanity.com/paper/2502.11420/) (2025)
- [GLASS Flows: Transition Sampling for Alignment of Flow and Diffusion Models](https://mlsanity.com/paper/2509.25170/) (2025)

## Built on by (most cited first, 1 of 1)

- [LATS: Levy Adaptive Tree Sampling for Feedback-Driven Diverse Target Discovery](https://mlsanity.com/paper/2609.06761/) (2026)

## Abstract (arXiv)

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.