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Most unsupervised domain adaptation (UDA) methods assume that labeled source images are available during model adaptation. However, this assumption is often infeasible owing to confidentiality issues or memory constraints on mobile devices. Some recently developed approaches do not require source images during adaptation, but they show limited performance on perturbed images. To address these problems, we propose a novel source-free UDA method that uses only a pre-trained source model and unlabeled target images. Our method captures the aleatoric uncertainty by incorporating data augmentation and trains the feature generator with two consistency objectives. The feature generator is encouraged to learn consistent visual features away from the decision boundaries of the head classifier. Thus, the adapted model becomes more robust to image perturbations. Inspired by self-supervised learning, our method promotes inter-space alignment between the prediction space and the feature space while incorporating intra-space consistency within the feature space to reduce the domain gap between the source and target domains. We also consider epistemic uncertainty to boost the model adaptation performance. Extensive experiments on popular UDA benchmark datasets demonstrate that the proposed source-free method is comparable or even superior to vanilla UDA methods. Moreover, the adapted models show more robust results when input images are perturbed.