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Creating accurate spatial representations that take into account uncertainty is critical for autonomous robots to safely navigate in unstructured environments. Although recent LIDAR based mapping techniques can produce robust occupancy maps, learning the parameters of such models demand considerable computational time, discouraging them from being used in real-time and large-scale applications such as autonomous driving. Recognizing the fact that real-world structures exhibit similar geometric features across a variety of urban environments, in this paper, we argue that it is redundant to learn all geometry dependent parameters from scratch. Instead, we propose a theoretical framework building upon the theory of optimal transport to adapt model parameters to account for changes in the environment, significantly amortizing the training cost. Further, with the use of high-fidelity driving simulators and real-world datasets, we demonstrate how parameters of 2D and 3D occupancy maps can be automatically adapted to accord with local spatial changes. We validate various domain adaptation paradigms through a series of experiments, ranging from inter-domain feature transfer to simulation-to-real-world feature transfer. Experiments verified the possibility of estimating parameters with a negligible computational and memory cost, enabling large-scale probabilistic mapping in urban environments.