提出分支薛定谔桥匹配，可模拟多路径演化过程。
Branched Schrödinger Bridge Matching
- 用多个时变速度场和生长过程建模分支演化路径
- 能准确捕捉从同一起点到多个终点的分化过程
- 适合细胞命运决定、多路径导航等复杂演化任务
预测初始分布与目标分布之间的中间轨迹是生成建模的核心问题。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来学习分布间映射，但本质上仅限于单峰转换，无法捕捉从共同起源向多个不同模式分叉的演化过程。为此，我们提出分支薛定谔桥匹配（BranchSBM），一种新型框架，可学习分支薛定谔桥。BranchSBM参数化多个时变速度场与增长过程，能够表示群体层面的分化，演化至多个终端分布。我们证明，BranchSBM不仅表达能力更强，而且在涉及多路径表面导航、从同质前体状态建模细胞命运分叉以及模拟细胞对扰动的分歧响应等任务中至关重要。
原文摘要 · Abstract (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 Schrödinger 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 modes. To address this, we introduce Branched Schrödinger Bridge Matching (BranchSBM), a novel framework that learns branched Schrödinger 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.
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