Distribution-Conditioned Transport
This work addresses the problem of generalizing transport models to unseen distribution pairs, which is crucial for scientific applications requiring robust models for diverse data distributions.
This paper introduces Distribution-Conditioned Transport (DCT), a framework that learns transport models conditioned on embeddings of source and target distributions. This enables generalization to unseen distribution pairs and semi-supervised learning for distributional forecasting. The framework is demonstrated on synthetic benchmarks and four biological applications, including batch effect transfer in single-cell genomics and perturbation prediction from mass cytometry data.
Learning a transport model that maps a source distribution to a target distribution is a canonical problem in machine learning, but scientific applications increasingly require models that can generalize to source and target distributions unseen during training. We introduce distribution-conditioned transport (DCT), a framework that conditions transport maps on learned embeddings of source and target distributions, enabling generalization to unseen distribution pairs. DCT also allows semi-supervised learning for distributional forecasting problems: because it learns from arbitrary distribution pairs, it can leverage distributions observed at only one condition to improve transport prediction. DCT is agnostic to the underlying transport mechanism, supporting models ranging from flow matching to distributional divergence-based models (e.g. Wasserstein, MMD). We demonstrate the practical performance benefits of DCT on synthetic benchmarks and four applications in biology: batch effect transfer in single-cell genomics, perturbation prediction from mass cytometry data, learning clonal transcriptional dynamics in hematopoiesis, and modeling T-cell receptor sequence evolution.