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Data-driven techniques for machine vision heavily depend on the training data to sufficiently resemble the data occurring during test and application. However, in practice unknown distortion can lead to a domain gap between training and test data, impeding the performance of a machine vision system. With our proposed approach this domain gap can be closed by unpaired learning of the pristine-to-distortion mapping function of the unknown distortion. This learned mapping function may then be used to emulate the unknown distortion in the training data. Employing a fixed setup, our approach is independent from prior knowledge of the distortion. Within this work, we show that we can effectively learn unknown distortions at arbitrary strengths. When applying our approach to instance segmentation in an autonomous driving scenario, we achieve results comparable to an oracle with knowledge of the distortion. An average gain in mean Average Precision (mAP) of up to 0.19 can be achieved.