Clustering is one of the fundamental tasks in computer vision and pattern recognition. Recently, deep clustering methods (algorithms based on deep learning) have attracted wide attention with their impressive performance. Most of these algorithms combine deep unsupervised representation learning and standard clustering together. However, the separation of representation learning and clustering will lead to suboptimal solutions because the two-stage strategy prevents representation learning from adapting to subsequent tasks (e.g., clustering according to specific cues). To overcome this issue, efforts have been made in the dynamic adaption of representation and cluster assignment, whereas current state-of-the-art methods suffer from heuristically constructed objectives with the representation and cluster assignment alternatively optimized. To further standardize the clustering problem, we audaciously formulate the objective of clustering as finding a precise feature as the cue for cluster assignment. Based on this, we propose a general-purpose deep clustering framework, which radically integrates representation learning and clustering into a single pipeline for the first time. The proposed framework exploits the powerful ability of recently developed generative models for learning intrinsic features, and imposes an entropy minimization on the distribution of the cluster assignment by a dedicated variational algorithm. The experimental results show that the performance of the proposed method is superior, or at least comparable to, the state-of-the-art methods on the handwritten digit recognition, fashion recognition, face recognition, and object recognition benchmark datasets.