Clustering is a popular unsupervised machine learning and data mining problem defined as a process of assigning objects to groups so that objects in the same group are similar to each other and differ from objects in other groups. In this paper, a data clustering method is proposed that is based on unsupervised training of a generative neural network using the technique of Implicit Maximum Likelihood Estimation (IMLE). Given a dataset, IMLE is an unsupervised method that trains a neural network that takes random noise as input and produces synthetic data samples whose distribution is close to the original data. We have developed an appropriate adaptation of the IMLE generative approach that also achieves clustering of the dataset. The proposed clustering method has been evaluated on several popular datasets of various types and complexity yielding promising results.