In this work, we propose a novel end-to-end sinkhorn autoencoder with noise generator for efficient data collection simulation. Simulating processes that aim at collecting experimental data is crucial for multiple real-life applications, including nuclear medicine, astronomy and high energy physics. Contemporary methods, such as Monte Carlo algorithms, provide high-fidelity results at a price of high computational cost. Multiple attempts are taken to reduce this burden, e.g. using generative approaches based on Generative Adversarial Networks or Variational Autoencoders. Although such methods 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 method 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. We optimise the entire model jointly. Our method outperforms competing approaches on a challenging dataset of simulation data from Zero Degree Calorimeters of ALICE experiment in LHC. as well as standard benchmarks, such as MNIST and CelebA.