Simulating detectors response is a crucial task in HEP experiments. Currently employed methods, such as Monte Carlo algorithms, provide high-fidelity results at a price of high computational cost, especially for dense detectors such as ZDC calorimeter in ALICE experiment. Multiple attempts are taken to reduce this burden, e.g. using generative approaches based on Generative Adversarial Networks or Variational Autoencoders. In this talk we will present adaptation of those stat-of-the-art methods for calorimeters response simulations. Although GANs and VAE are much faster, they are often unstable in training and do not allow sampling from an entire data distribution. To address these shortcomings, we introduce a novel generative model dubbed end-to-end sinkhorn autoencoder that leverages sinkhorn algorithm to explicitly align distribution of encoded real data examples and generated noise. More precisely, we extend autoencoder architecture by adding a deterministic neural network trained to map noise from a known distribution onto autoencoder latent space representing data distribution. Our method outperforms competing approaches on the challenging dataset of simulation data from Zero Degree Calorimeters of ALICE experiment in LHC. as well as standard benchmarks, such as MNIST and CelebA.