分支薛定谔橋接匹配

摘要

预测初始分布与目标分布之间的中间轨迹是生成建模中的一个核心问题。现有方法，如流匹配和薛定谔桥匹配，通过建模单一随机路径，有效地学习两个分布之间的映射。然而，这些方法本质上局限于单模态过渡，无法捕捉从共同起源到多个不同结果的分支或发散演化。为了解决这一问题，我们引入了分支薛定谔桥匹配（BranchSBM），这是一个新颖的框架，能够学习分支薛定谔桥。BranchSBM参数化多个时间依赖的速度场和增长过程，从而能够表示群体水平向多个终端分布的发散。我们展示了BranchSBM不仅在表达上更为丰富，而且在涉及多路径表面导航、从同质祖细胞状态建模细胞命运分叉以及模拟细胞对扰动的发散反应等任务中也是必不可少的。

English

Predicting the intermediate trajectories between an initial and target distribution is a central problem in generative modeling. Existing approaches, such as flow matching and Schr\"odinger Bridge Matching, effectively learn mappings between two distributions by modeling a single stochastic path. However, these methods are inherently limited to unimodal transitions and cannot capture branched or divergent evolution from a common origin to multiple distinct outcomes. To address this, we introduce Branched Schr\"odinger Bridge Matching (BranchSBM), a novel framework that learns branched Schr\"odinger bridges. BranchSBM parameterizes multiple time-dependent velocity fields and growth processes, enabling the representation of population-level divergence into multiple terminal distributions. We show that BranchSBM is not only more expressive but also essential for tasks involving multi-path surface navigation, modeling cell fate bifurcations from homogeneous progenitor states, and simulating diverging cellular responses to perturbations.

分支薛定谔橋接匹配

Branched Schrödinger Bridge Matching

摘要

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