Modern deep learning methods have achieve remarkable performance on a variety of computer vision tasks, but frequently require large, well-balanced training datasets to achieve high-quality results. Data-efficient performance is critical for downstream tasks such as automated driving or facial recognition. We propose two methods of data-efficient learning for the tasks of image synthesis and instance segmentation. We first propose a method of high-quality and diverse image generation from finetuning to only 5-100 images. Our method factors a pretrained model into a small but highly expressive weight space for finetuning, which discourages overfitting in a small training set. We validate our method in a challenging few-shot setting of 5-100 images in the target domain. We show that our method has significant visual quality gains compared with existing GAN adaptation methods. Next, we introduce a simple adaptive instance segmentation loss which achieves state-of-the-art results on the LVIS dataset. We demonstrate that the rare categories are heavily suppressed by textit{correct background predictions}, which reduces the probability for all foreground categories with equal weight. Due to the relative infrequency of rare categories, this leads to an imbalance that biases towards predicting more frequent categories. Based on this insight, we develop DropLoss -- a novel adaptive loss to compensate for this imbalance without a trade-off between rare and frequent categories.