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.

翻译：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转移，无法捕捉从共同起源到多个不同模式的分支或发散演化。为解决此问题，我们引入了分支薛定谔桥匹配（BranchSBM），这是一个学习分支薛定谔桥的新颖框架。BranchSBM参数化了多个时间相关的速度场和增长过程，从而能够表示群体水平上向多个终端分布的发散。我们证明，BranchSBM不仅更具表达力，而且对于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响应等任务至关重要。