We aim to build image generation models that generalize to new domains from few examples. To this end, we first investigate the generalization properties of classic image generators, and discover that autoencoders generalize extremely well to new domains, even when trained on highly constrained data. We leverage this insight to produce a robust, unsupervised few-shot image generation algorithm, and introduce a novel training procedure based on recovering an image from data augmentations. Our Augmentation-Interpolative AutoEncoders synthesize realistic images of novel objects from only a few reference images, and outperform both prior interpolative models and supervised few-shot image generators. Our procedure is simple and lightweight, generalizes broadly, and requires no category labels or other supervision during training.