Shortest-Path Flow Matching with Mixture-Conditioned Bases for Unseen-Condition Generalization

Robust generalization under distribution shift remains a key challenge for conditional generative modeling: conditional flow-based methods often fit the training conditions well but fail to extrapolate to unseen ones. This is particularly important for therapeutic prioritization, where the goal is to predict cellular responses to unseen candidate drugs and genetic perturbations in order to select the most effective intervention. We introduce SP-FM, a shortest-path flow-matching framework that improves generalization to unseen conditions by conditioning both the base distribution and the flow field on the condition. Specifically, SP-FM learns a condition-dependent base distribution parameterized as a flexible, learnable mixture, together with a condition-dependent vector field trained via shortest-path flow matching. Conditioning the base allows the model to adapt its starting distribution across conditions, enabling smooth interpolation and more reliable extrapolation beyond the observed training range. We provide theoretical insights into the resulting conditional transport and show how mixture-conditioned bases enhance robustness under shift. Empirically, SP-FM is effective across heterogeneous domains, including predicting responses to unseen perturbations in single-cell transcriptomics and modeling treatment effects in microscopy-based drug screening. Overall, SP-FM provides a simple yet effective plug-in strategy for improving conditional generative modeling and generalization to unseen conditions.