Data augmentation has led to substantial improvements in the performance and generalization of deep models, and remain a highly adaptable method to evolving model architectures and varying amounts of data---in particular, extremely scarce amounts of available training data. In this paper, we present a novel method of applying Mobius transformations to augment input images during training. Mobius transformations are bijective conformal maps that generalize image translation to operate over complex inversion in pixel space. As a result, Mobius transformations can operate on the sample level and preserve data labels. We show that the inclusion of Mobius transformations during training enables improved generalization over prior sample-level data augmentation techniques such as cutout and standard crop-and-flip transformations, most notably in low data regimes.