The lack of labeled background data makes a big performance gap between cosine and Probabilistic Linear Discriminant Analysis (PLDA) scoring baseline techniques for i-vectors in speaker recognition. Although there are some unsupervised clustering techniques to estimate the labels, they cannot accurately predict the true labels and they also assume that there are several samples from the same speaker in the background data that could not be true in reality. In this paper, the authors make use of Deep Learning (DL) to fill this performance gap given unlabeled background data. To this goal, the authors have proposed an impostor selection algorithm and a universal model adaptation process in a hybrid system based on deep belief networks and deep neural networks to discriminatively model each target speaker. In order to have more insight into the behavior of DL techniques in both single- and multisession speaker enrollment tasks, some experiments have been carried out in this paper in both scenarios. Experiments on National Institute of Standards and Technology 2014 i-vector challenge show that 46% of this performance gap, in terms of minimum of the decision cost function, is filled by the proposed DL-based system. Furthermore, the score combination of the proposed DL-based system and PLDA with estimated labels covers 79% of this gap.