The existence of leakage current pathways leading to the appearance of impact ionization and the potential device breakdown in planar Gunn GaN diodes is analyzed by means of a combined Monte Carlo-deep learning approach. Front-view (lateral) Monte Carlo simulations of the devices show the appearance of a high-field hotspot at the anode corner of the etched region, just at the boundaries between the dielectric, the GaN-doped layer, and the buffer. Thus, if the isolation created by the etched trenches is not complete, a relevant hot carrier population within the buffer is observed at sufficiently high applied voltages, provoking the appearance of a very significant number of impact ionizations and the consequent avalanche process before the onset of Gunn oscillations. A neural network trained from Monte Carlo simulations allows predicting with extremely good precision the breakdown voltage of the diodes depending on the doping of the GaN active layer, the permittivity of the isolating dielectric, and the lattice temperature. Low doping, high temperature and high permittivity provide larger operational voltages, which implies a tradeoff with the conditions required to achieve THz Gunn oscillations at low voltages.