In order to achieve efficient similarity searching, hash functions are designed to encode images into low-dimensional binary codes with the constraint that similar features will have a short distance in the projected Hamming space. Recently, deep learning-based methods have become more popular, and outperform traditional non-deep methods. However, without label information, most state-of-the-art unsupervised deep hashing (DH) algorithms suffer from severe performance degradation for unsupervised scenarios. One of the main reasons is that the ad-hoc encoding process cannot properly capture the visual feature distribution. In this paper, we propose a novel unsupervised framework that has two main contributions: 1) we convert the unsupervised DH model into supervised by discovering pseudo labels; 2) the framework unifies likelihood maximization, mutual information maximization, and quantization error minimization so that the pseudo labels can maximumly preserve the distribution of visual features. Extensive experiments on three popular data sets demonstrate the advantages of the proposed method, which leads to significant performance improvement over the state-of-the-art unsupervised hashing algorithms.