Single-cell genomics has significantly advanced our understanding of cellular behavior, catalyzing innovations in treatments and precision medicine. However, single-cell sequencing technologies are inherently destructive and can only measure a limited range of data modalities simultaneously. This limitation underscores the need for new methods capable of realigning cells. Optimal transport (OT) has emerged as a powerful solution, but traditional discrete solvers are hampered by scalability, privacy, and out-of-sample estimation issues. These challenges have spurred the development of neural network-based solvers, known as neural OT solvers, that parameterize OT maps. However, these models often lack the flexibility needed for broader life science applications. To address these shortcomings, our approach learns stochastic maps (i.e., transportation plans), allows for any cost function, relaxes mass conservation constraints, and integrates quadratic solvers to address the complex challenges posed by the Gromov-(merged) problem. Wasserstein. Using flow matching as the backbone, our method offers a flexible and efficient framework. We demonstrate its versatility and robustness through applications in cell development studies, cellular drug response modeling, and cellular translation across modalities, illustrating significant potential for improving therapeutic strategies.
