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We propose a domain adaptation method, MoDA, which adapts a pretrained embodied agent to a new, noisy environment without ground-truth supervision. Map-based memory provides important contextual information for visual navigation, and exhibits unique spatial structure mainly composed of flat walls and rectangular obstacles. Our adaptation approach encourages the inherent regularities on the estimated maps to guide the agent to overcome the prevalent domain discrepancy in a novel environment. Specifically, we propose an efficient learning curriculum to handle the visual and dynamics corruptions in an online manner, self-supervised with pseudo clean maps generated by style transfer networks. Because the map-based representation provides spatial knowledge for the agent's policy, our formulation can deploy the pretrained policy networks from simulators in a new setting. We evaluate MoDA in various practical scenarios and show that our proposed method quickly enhances the agent's performance in downstream tasks including localization, mapping, exploration, and point-goal navigation.