Passive seismic interferometry is a vastly generalized blind deconvolution question, where different paths through the Earth correspond to different channels called Green's functions; the sources are completely incoherent and not shared by the channels, and the question is to estimate paths (channels) that are not present in the dataset. SI, turning noise to signal, has numerous applications, from monitoring industrial activities to crustal structure investigation. No standard method of signal processing will solve SI. Instead, domain scientists resort to a simple cross-correlation operation, a.k.a. correlogram, which can retrieve the Green's function directly, but only under restrictive assumptions of ergodicity (energy equipartitioning) of the random process generating the seismic source. However, in practice, correlograms are not equal to the empirical Green's function, because these assumptions are generally far from being satisfied in realistic situations. In the framework of supervised learning, we propose to train deep neural networks (NNs) to overcome two limitations of correlation-based SI: the temporal limitation of passive recordings and the spatial limitation of the random source distribution. Deep NNs are trained to implicitly find the relationship between the empirical Green's functions and the correlograms and then used to extract the correct Green's functions from ambient noise. The input of the network is correlograms (a virtual shot gather), and the desired output is the empirical Green's function (the active shot gather). The NN can often retrieve Green's functions from 5-min passive recordings with acceptable accuracy in our synthetic example. Although an exact estimation of the source locations may not be necessary, a prior knowledge of the source directionality (through a preliminary beamforming step) is helpful when training the NN to mitigate the challenges associated with inhomogeneous source distributions (directional wave fields). In this work, all the numerical examples are based on the retrieval of P-wave reflections in the exploration scale and are conducted on synthetic data. We use a modified ResNet in our numerical experiments.