In unsupervised learning, there is no apparent straightforward cost function that can capture the significant factors of variations and similarities. Since natural systems have smooth dynamics, an opportunity is lost if an unsupervised objective function remains static during the training process. The absence of concrete supervision suggests that smooth dynamics should be integrated. Compared to classical static cost functions, dynamic objective functions allow to better make use of the gradual and uncertain knowledge acquired through pseudo-supervision. In this paper, we propose Dynamic Autoencoder (DynAE), a novel model for deep clustering that overcomes a clustering-reconstruction trade-off, by gradually and smoothly eliminating the reconstruction objective function in favor of a construction one. Experimental evaluations on benchmark datasets show that our approach achieves state-of-the-art results compared to the most relevant deep clustering methods.