Gadolinium-loading of large water Cherenkov detectors is a prime method for the detection of the Diffuse Supernova Neutrino Background (DSNB). While the enhanced neutron tagging capability greatly reduces single-event backgrounds, correlated events mimicking the IBD coincidence signature remain a potentially harmful background. Neutral-Current (NC) interactions of atmospheric neutrinos potentially dominate the DSNB signal especially in the low-energy range of the observation window that reaches from about 12 to 30 MeV. The present paper investigates a novel method for the discrimination of this background. Convolutional Neural Networks (CNNs) offer the possibility for a direct analysis and classification of the PMT hit patterns of the prompt events. Based on the events generated in a simplified SuperKamiokande-like detector setup, we find that a trained CNN can maintain a signal efficiency of 96 % while reducing the residual NC background to 2 % of the original rate. Comparing to recent predictions of the DSNB signal and measurements of the NC background levels in Super-Kamiokande, the corresponding signal-to-background ratio is about 4:1, providing excellent conditions for a DSNB discovery.