Unsupervised learning of identity-discriminative visual feature is appealing in real-world tasks where manual labelling is costly. However, the images of an identity can be visually discrepant when images are taken under different states, e.g. different camera views and poses... This visual discrepancy leads to great difficulty in unsupervised discriminative learning. Fortunately, in real-world tasks we could often know the states without human annotation, e.g. we can easily have the camera view labels in person re-identification and facial pose labels in face recognition. In this work we propose utilizing the state information as weak supervision to address the visual discrepancy caused by different states. We formulate a simple pseudo label model and utilize the state information in an attempt to refine the assigned pseudo labels by the weakly supervised decision boundary rectification and weakly supervised feature drift regularization. We evaluate our model on unsupervised person re-identification and pose-invariant face recognition. Despite the simplicity of our method, it could outperform the state-of-the-art results on Duke-reID, MultiPIE and CFP datasets with a standard ResNet-50 backbone. We also find our model could perform comparably with the standard supervised fine-tuning results on the three datasets. Code is available at https://github.com/KovenYu/state-information (read more)