Many open-world applications require the detection of novel objects, yet state-of-the-art object detection and instance segmentation networks do not excel at this task. The key issue lies in their assumption that regions without any annotations should be suppressed as negatives, which teaches the model to treat the unannotated objects as background. To address this issue, we propose a simple yet surprisingly powerful data augmentation and training scheme we call Learning to Detect Every Thing (LDET). To avoid suppressing hidden objects, background objects that are visible but unlabeled, we paste annotated objects on a background image sampled from a small region of the original image. Since training solely on such synthetically augmented images suffers from domain shift, we decouple the training into two parts: 1) training the region classification and regression head on augmented images, and 2) training the mask heads on original images. In this way, a model does not learn to classify hidden objects as background while generalizing well to real images. LDET leads to significant improvements on many datasets in the open world instance segmentation task, outperforming baselines on cross-category generalization on COCO, as well as cross-dataset evaluation on UVO and Cityscapes.