Device-to-device (D2D) communication, which enables a direct connection between users while bypassing the cellular channels to base stations (BSs), is a promising way to offload the traffic from conventional cellular networks. In D2D communication, one recurring problem is that, in order to optimally allocate resources across D2D and cellular users, the knowledge of D2D channel gains is needed. However, such knowledge is hard to obtain at reasonable signaling costs. In this paper, we show this problem can be circumvented by tapping into the information provided by the estimation of the cellular channels between the users and surrounding BSs as this estimation is done anyway for a normal operation of the network. While the cellular and D2D channel gains exhibit independent fast fading behavior, we show that average gains of the cellular and D2D channels share a non-explicit correlation structure, which is rooted into the network topology, terrain, and buildings setup. We propose a machine (deep) learning approach capable of predicting the D2D channel gains from seemingly independent cellular channels. Our results show a high degree of convergence between true and predicted D2D channel gains. The predicted gains allow to reach a near-optimal communication capacity in many radio resource management algorithms.