  The domain discrepancy existed between medical images acquired in different
situations renders a major hurdle in deploying pre-trained medical image
segmentation models for clinical use. Since it is less possible to distribute
training data with the pre-trained model due to the huge data size and privacy
concern, source-free unsupervised domain adaptation (SFDA) has recently been
increasingly studied based on either pseudo labels or prior knowledge. However,
the image features and probability maps used by pseudo label-based SFDA and the
consistent prior assumption and the prior prediction network used by
prior-guided SFDA may become less reliable when the domain discrepancy is
large. In this paper, we propose a \textbf{Pro}mpt learning based \textbf{SFDA}
(\textbf{ProSFDA}) method for medical image segmentation, which aims to improve
the quality of domain adaption by minimizing explicitly the domain discrepancy.
Specifically, in the prompt learning stage, we estimate source-domain images
via adding a domain-aware prompt to target-domain images, then optimize the
prompt via minimizing the statistic alignment loss, and thereby prompt the
source model to generate reliable predictions on (altered) target-domain
images. In the feature alignment stage, we also align the features of
target-domain images and their styles-augmented counterparts to optimize the
source model, and hence push the model to extract compact features. We evaluate
our ProSFDA on two multi-domain medical image segmentation benchmarks. Our
results indicate that the proposed ProSFDA outperforms substantially other SFDA
methods and is even comparable to UDA methods. Code will be available at
\url{https://github.com/ShishuaiHu/ProSFDA}.
