Distribution-Conditioned Transport

TL;DR

Distribution-conditioned transport (DCT) is a novel framework that enables transport models to generalize across unseen source and target distributions by conditioning on learned distribution embeddings, improving performance in diverse scientific applications.

Contribution

We introduce DCT, a flexible framework that conditions transport maps on distribution embeddings, allowing generalization to unseen pairs and semi-supervised learning across various transport mechanisms.

Findings

DCT outperforms existing methods on synthetic benchmarks.

DCT improves biological data analysis tasks such as batch effect transfer.

DCT demonstrates versatility across multiple scientific applications.

Abstract

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.