Existing beamforming-based full-duplex solutions for multi-antenna wireless systems often rely on explicit estimation of the self-interference channel. The pilot overhead of such estimation, however, can be prohibitively high in millimeter-wave and massive MIMO systems, thus limiting the practicality of existing solutions, especially in fast-fading conditions. In this work, we present a novel beam learning framework that bypasses explicit self-interference channel estimation by designing beam codebooks to efficiently obtain implicit channel knowledge that can then be processed by a deep learning network to synthesize transmit and receive beams for full-duplex operation. Simulation results using ray-tracing illustrate that our proposed technique can allow a full-duplex base station to craft serving beams that couple low self-interference while delivering high SNR, with 75-97% fewer measurements than would be required for explicit estimation of the self-interference channel.