Real world datasets naturally contain variability whose origin is in varying conditions of measurement instruments, augmenting the variability of the physical phenomena of interest. An important example is biological data, where differences in the calibration of the measuring instrument might be an obstacle to valid and effective statistical analysis, for example when comparing measurements obtained from two identical instruments, or even from the same instrument at different times. In this manuscript we propose a deep learning approach for overcoming such calibration differences, by learning a map that matches two multi-dimensional distributions, measured in two different batches. We apply our method to real world CyTOF and single-cell RNA-seq datasets, notoriously subject to instrument calibration effects, and demonstrate its effectiveness to calibrate identical replicated samples, by removing batch effects that cannot be eliminated satisfactory using existing methods. Furthermore, our experiments suggest that a network that was trained on a replicates of one sample measured in two different batches can effectively calibrate data of other samples, hence eliminate batch effects.