Label assignment in object detection aims to assign targets, foreground or background, to sampled regions in an image. Unlike labeling for image classification, this problem is not well defined due to the objects bounding box. In this paper, we investigate the problem from a perspective of distillation, hence we call Label Assignment Distillation (LAD). Our initial motivation is very simple, we use a teacher network to generate labels for the student. This can be achieved in two ways: either using the teachers prediction as the direct targets (soft label), or through the hard labels dynamically assigned by the teacher (LAD). Our experiments reveal that: (i) LAD is more effective than soft-label, but they are complementary. (ii) Using LAD, a smaller teacher can also improve a larger student significantly, while soft-label cant. We then introduce Co-learning LAD, in which two networks simultaneously learn from scratch and the role of teacher and student are dynamically interchanged. Using PAA-ResNet50 as a teacher, our LAD techniques can improve detectors PAA-ResNet101 and PAA-ResNeXt101 to $46 rm AP$ and $47.5rm AP$ on the COCO test-dev set. With a strong teacher PAA-SwinB, we improve the PAA-ResNet50 to $43.9rm AP$ with only 1x schedule training, and PAA-ResNet101 to $47.9rm AP$, significantly surpassing the current methods. Our source code and checkpoints will be released at https://github.com/cybercore-co-ltd/CoLAD_paper.