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In this paper, we propose a framework capable of generating face images that fall into the same distribution as that of a given one-shot example. We leverage a pre-trained StyleGAN model that already learned the generic face distribution. Given the one-shot target, we develop an iterative optimization scheme that rapidly adapts the weights of the model to shift the output's high-level distribution to the target's. To generate images of the same distribution, we introduce a style-mixing technique that transfers the low-level statistics from the target to faces randomly generated with the model. With that, we are able to generate an unlimited number of faces that inherit from the distribution of both generic human faces and the one-shot example. The newly generated faces can serve as augmented training data for other downstream tasks. Such setting is appealing as it requires labeling very few, or even one example, in the target domain, which is often the case of real-world face manipulations that result from a variety of unknown and unique distributions, each with extremely low prevalence. We show the effectiveness of our one-shot approach for detecting face manipulations and compare it with other few-shot domain adaptation methods qualitatively and quantitatively.