发表机构
MBZUAI（穆罕默德·本·扎耶德人工智能大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种可扩展的分支流匹配算法，将Benamou-Brenier公式改编为分支生成流，以解决高维分支最优传输问题，并在生物和图像生成任务中验证其有效性。
AI 中文摘要
分支最优传输（Branched Optimal Transport, BOT）方法模拟了自然树状结构（如河流和生物系统中发现的那些结构）的经济性和高效性。这些方法广泛适用于设计社会中的高效网络，从流域和血管到邮件和燃气分配系统。然而，在设计深度生成模型（尤其是在大规模场景下）的背景下，它们仍研究不足。标准的连续时间生成模型，如流匹配（flow matching）方法，无法捕捉现实世界数据中固有的层次和分支模式。当前模型没有提供让流合并或共享路径以最小化总传输成本的机制。受BOT中“规模经济”原理的启发，我们引入了一种新颖的、可扩展的分支流匹配算法，旨在解决高维空间中的分支最优传输问题。我们的方法改编了Benamou-Brenier连续时间最优传输公式，以学习分支生成流。这些流允许概率质量沿共同路径聚合，然后再分支到不同的目标。通过神经网络进行参数化，我们的方法有效地学习了复杂的分支生成过程。我们在生物学和图像生成领域具有挑战性的高维任务中展示了其有效性。
英文摘要
Methods of Branched Optimal Transport (BOT) mimic the economy and efficiency of natural tree-like structures, such as those found in rivers and biological systems. These methods are widely applicable for designing efficient networks in society, from river basins and blood vessels to mail and gas distribution systems. However, they remain understudied in the context of designing deep generative models, particularly at a large scale. Standard continuous-time generative models, such as the flow matching approach, fail to capture the inherent hierarchical and branching patterns present in real-world data. Current models provide no mechanism for flows to merge or share pathways to minimize total transport cost. Inspired by the "economy of scale" principle in BOT, we introduce a novel, scalable branched flow-matching algorithm designed to solve the branched optimal transport problem in high dimensions. Our method adapts the Benamou-Brenier continuous-time optimal transport formulation to learn branched generative flows. These flows allow probability mass to aggregate along common pathways before branching out to diverse targets. Parametrized by neural networks, our method effectively learns complex branched generative processes. We demonstrate its effectiveness on challenging high-dimensional tasks in biology and image generation.
