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We study the problem of weakly semi-supervised object detection with points (WSSOD-P), where the training data is combined by a small set of fully annotated images with bounding boxes and a large set of weakly-labeled images with only a single point annotated for each instance. The core of this task is to train a point-to-box regressor on well-labeled images that can be used to predict credible bounding boxes for each point annotation. We challenge the prior belief that existing CNN-based detectors are not compatible with this task. Based on the classic R-CNN architecture, we propose an effective point-to-box regressor: Group R-CNN. Group R-CNN first uses instance-level proposal grouping to generate a group of proposals for each point annotation and thus can obtain a high recall rate. To better distinguish different instances and improve precision, we propose instance-level proposal assignment to replace the vanilla assignment strategy adopted in the original R-CNN methods. As naive instance-level assignment brings converging difficulty, we propose instance-aware representation learning which consists of instance-aware feature enhancement and instance-aware parameter generation to overcome this issue. Comprehensive experiments on the MS-COCO benchmark demonstrate the effectiveness of our method. Specifically, Group R-CNN significantly outperforms the prior method Point DETR by 3.9 mAP with 5% well-labeled images, which is the most challenging scenario. The source code can be found at https://github.com/jshilong/GroupRCNN