In the past decades, great progress has been made in the field of optical and particle-based measurement techniques for experimental analysis of fluid flows. Particle Image Velocimetry (PIV) technique is widely used to identify flow parameters from time-consecutive snapshots of particles injected into the fluid. The computation is performed as post-processing of the experimental data via proximity measure between particles in frames of reference. However, the post-processing step becomes problematic as the motility and density of the particles increases, since the data emerges in extreme rates and volumes. Moreover, existing algorithms for PIV either provide sparse estimations of the flow or require large computational time frame preventing from on-line use. The goal of this manuscript is therefore to develop an accurate on-line algorithm for estimation of the fine-grained velocity field from PIV data. As the data constitutes a pair of images, we employ computer vision methods to solve the problem. In this work, we introduce a convolutional neural network adapted to the problem, namely Volumetric Correspondence Network (VCN) which was recently proposed for the end-to-end optical flow estimation in computer vision. The network is thoroughly trained and tested on a dataset containing both synthetic and real flow data. Experimental results are analyzed and compared to that of conventional methods as well as other recently introduced methods based on neural networks. Our analysis indicates that the proposed approach provides improved efficiency also keeping accuracy on par with other state-of-the-art methods in the field. We also verify through a-posteriori tests that our newly constructed VCN schemes are reproducing well physically relevant statistics of velocity and velocity gradients.