Departures: Distributional Transport for Single-Cell Perturbation Prediction with Neural Schr"odinger Bridges

Predicting single-cell perturbation outcomes directly advances gene function analysis and facilitates drug candidate selection, making it a key driver of both basic and translational biomedical research. However, a major bottleneck in this task is the unpaired nature of single-cell data, as the same cell cannot be observed both before and after perturbation due to the destructive nature of sequencing. Although some neural generative transport models attempt to tackle unpaired single-cell perturbation data, they either lack explicit conditioning or depend on prior spaces for indirect distribution alignment, limiting precise perturbation modeling. In this work, we approximate Schr"odinger Bridge (SB), which defines stochastic dynamic mappings recovering the entropy-regularized optimal transport (OT), to directly align the distributions of control and perturbed single-cell populations across different perturbation conditions. Unlike prior SB approximations that rely on bidirectional modeling to infer optimal source-target sample coupling, we leverage Minibatch-OT based pairing to avoid such bidirectional inference and the associated ill-posedness of defining the reverse process. This pairing directly guides bridge learning, yielding a scalable approximation to the SB. We approximate two SB models, one modeling discrete gene activation states and the other continuous expression distributions. Joint training enables accurate perturbation modeling and captures single-cell heterogeneity. Experiments on public genetic and drug perturbation datasets show that our model effectively captures heterogeneous single-cell responses and achieves state-of-the-art performance.