Shortest-Path Flow Matching with Mixture-Conditioned Bases for OOD Generalization to Unseen Conditions

TL;DR

SP-FM introduces a shortest-path flow-matching framework that conditions both the base distribution and flow field on the condition, significantly enhancing out-of-distribution generalization for conditional generative models.

Contribution

It proposes a novel condition-dependent base distribution with a learnable mixture and a shortest-path flow matching approach, improving robustness and extrapolation in conditional generative modeling.

Findings

Effective in predicting responses to unseen perturbations in transcriptomics.

Models treatment effects in high-content microscopy.

Enhances robustness under distribution shift.

Abstract

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. We introduce SP-FM, a shortest-path flow-matching framework that improves out-of-distribution (OOD) generalization 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 high-content microscopy--based drug screening. Overall, SP-FM provides a simple yet effective plug-in strategy for improving conditional generative modeling and OOD generalization across diverse domains.