Simulating the detector response is a key component of every highenergy physics experiment. The methods used currently for this purpose provide high-fidelity results. However, this precision comes at a price of a high computational cost. In this work, we introduce our research aiming at fast generation of the possible responses of detector clusters to particle collisions. We present the results for the real-life example of the Time Projection Chamber in the ALICE experiment at CERN. The essential component of our solution is a generative model that allows to simulate synthetic data points that bear high similarity to the real data. Leveraging recent advancements in machine learning, we propose to use conditional Generative Adversarial Networks. In this work we present a method to simulate data samples possible to record in the detector based on the initial information about particles. We propose and evaluate several models based on convolutional or recursive networks. The main advantage offered by the proposed method is a significant speed-up in the execution time, reaching up to the factor of $10^2$ with respect to the currently used simulation tool. Nevertheless, this speed-up comes at a price of a lower simulation quality. In this work we adapt available methods and show their quantitative and qualitative limitations.