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High energy physics experiments rely heavily on the detailed detector simulation models in many tasks. Running these detailed models typically requires a notable amount of the computing time available to the experiments. In this work, we demonstrate a new approach to speed up the simulation of the Time Projection Chamber tracker of the MPD experiment at the NICA accelerator complex. Our method is based on a Generative Adversarial Network - a deep learning technique allowing for implicit estimation of the population distribution for a given set of objects. This approach lets us learn and then sample from the distribution of raw detector responses, conditioned on the parameters of the charged particle tracks. To evaluate the quality of the proposed model, we integrate a prototype into the MPD software stack and demonstrate that it produces high-quality events similar to the detailed simulator, with a speed-up of at least an order of magnitude. The prototype is trained on the responses from the inner part of the detector and, once expanded to the full detector, should be ready for use in physics tasks.