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Most existing methods for unsupervised domain adaptation (UDA) rely on a shared network to extract domain-invariant features. However, when facing multiple source domains, optimizing such a network involves updating the parameters of the entire network, making it both computationally expensive and challenging, particularly when coupled with min-max objectives. Inspired by recent advances in prompt learning that adapts high-capacity models for downstream tasks in a computationally economic way, we introduce Multi-Prompt Alignment (MPA), a simple yet efficient 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. Then, MPA denoises the learned prompts through an auto-encoding process and aligns them by maximizing the agreement of all the reconstructed prompts. Moreover, we show that the resulting subspace acquired from the auto-encoding process can easily generalize to a streamlined set of target domains, making our method more efficient for practical usage. Extensive experiments show that MPA achieves state-of-the-art results on three popular datasets with an impressive average accuracy of 54.1% on DomainNet.