Title: Multi-Prompt Alignment for Multi-source Unsupervised Domain Adaptation. Abstract: Most existing methods for multi-source unsupervised domain adaptation (UDA) rely on a common feature encoder to extract domain-invariant features. However, learning such an encoder involves updating the parameters of the entire network, which makes the optimization computationally expensive, particularly when coupled with min-max objectives. Inspired by recent advances in prompt learning that adapts high-capacity deep models for downstream tasks in a computationally economic way, we introduce Multi-Prompt Alignment (MPA), a simple yet efficient two-stage framework for multi-source UDA. Given a source and target domain pair, MPA first trains an individual prompt to minimize the domain gap through a contrastive loss, while tuning only a small set of parameters. Then, MPA derives a low-dimensional latent space through an auto-encoding process that maximizes the agreement of multiple learned prompts. The resulting embedding further facilitates generalization to unseen domains. Extensive experiments show that our method achieves state-of-the-art results on popular benchmark datasets while requiring substantially fewer tunable parameters. To the best of our knowledge, we are the first to apply prompt learning to the multi-source UDA problem and our method achieves the highest reported average accuracy of 54.1% on DomainNet, the most challenging UDA dataset to date, with only 15.9M parameters trained. More importantly, we demonstrate that the learned embedding space can be easily adapted to novel unseen domains.