Inference problems for two-dimensional snapshots of rotating turbulent flows are studied. We perform a systematic quantitative benchmark of point-wise and statistical reconstruction capabilities of linear Extended Proper Orthogonal Decomposition (EPOD) method, the nonlinear Convolutional Neural Network (CNN) and the same CNN but embedding in a Generative Adversarial Network (GAN). We attack the important task of inferring one velocity component out of the measurement of a second one, and two cases are considered: (I) when both components lie in the plane orthogonal to the rotation axis and (II) one of the two is in the rotational direction. We show that EPOD works well only for the former case, when both components are strongly correlated, while CNN and GAN always outperform EPOD both concerning point-wise and statistical reconstructions. For case (II), when the input and output data are weakly correlated, all methods fail to reconstruct faithfully the point-wise information. In this case, only GAN is able to reconstruct the field in a statistical sense. The analysis is performed using both standard validation tools based on L_2 spatial distance between the prediction and the ground truth and more sophisticated multi-scale analysis using wavelet decomposition. Statistical validation is based on standard Jensen-Shannon divergence between the probability density functions, spectral properties and multi-scale flatness. This work was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 882340).