This paper aims to enhance the cascaded channel estimation process of intelligent reflecting surface (IRS)-aided communication systems while considering the detrimental effect of pilot signal contamination. When the transmitter is equipped with massive multiple-input multiple-output (mMIMO) antennas, and the IRS consists of a large number of reflecting elements, it is practically infeasible to allocate orthogonal pilots over each cascaded link, each consisting of a pair of antenna and reflecting elements. Reusing pilot signals over multiple parallel cascaded links causes interference, known as pilot contamination. Severe pilot contamination deteriorates the accuracy of the channel estimation process significantly. Accurate estimation of high-dimensional cascaded channels of IRS is crucial to distribute narrow beams in the desired direction, which becomes even more cumbersome in the presence of pilot contamination. To address this challenge, we propose deep learning-empowered two approaches to accurately estimate the channel gains of the cascaded links. Subsequently, learning from the correlation of the estimated cascaded links, we predict the cascaded links for other reflecting elements. Simulation results demonstrate the improved performance of the proposed techniques over the baseline schemes.