Learning word representations has garnered greater attention in the recent past due to its diverse text applications. Word embeddings encapsulate the syntactic and semantic regularities of words among sentences. Modelling word embedding as multi-sense gaussian mixture distributions will additionally capture uncertainty and polysemy of words. We propose to learn the Gaussian mixture representation of words using a Kullback-Leibler (KL) divergence based objective function. The KL divergence based energy function provides a better distance metric which can effectively capture entailment and distribution similarity among the words. Due to the intractability of KL divergence for Gaussian mixture, we go for a KL approximation between Gaussian mixtures. We train on a Wikipedia based dataset and perform qualitative and quantitative experiments on benchmark word similarity and entailment datasets which demonstrate the effectiveness of the proposed approach. © 2021 ACM.