Learning Heterogeneous Single-Cell Perturbation Responses with Moment-Conditioned Schrödinger Transport

Single-cell perturbation models aim to predict the cellular consequences of genetic interventions beyond experimentally observed conditions. While condition-level predictors can accurately estimate the aggregate transcriptional response, a single response moment does not determine the heterogeneous population of cellular outcomes observed by single-cell assays. The resulting challenge is to infer a full response distribution that is simultaneously consistent with the predicted perturbation effect and faithful to population structure learned from observed cells. We propose Moment-Conditioned Schrödinger Transport, a framework that couples condition-level perturbation prediction with stochastic population modeling. Our formulation decomposes a perturbation response into a prescribed condition moment and a centered population law, and learns the latter directly from empirical control and treated populations. A response-aware geometry represents both perturbation-associated shifts and within-condition heterogeneity, while a conditional Schr\"odinger bridge learns transferable stochastic transport under a Brownian reference. Moment-consistent recovery then reconstructs expression-space populations while retaining the prescribed perturbation response. Across established single-cell perturbation benchmarks and challenging generalization to unseen interventions and cellular contexts, our approach consistently improves both perturbation-response fidelity and distributional accuracy over strong predictive, generative, and transport baselines. Controlled analyses further demonstrate recovery of population variability and joint response structure beyond what is specified by condition-level prediction alone.