The de novo design of antimicrobial therapeutics involves the exploration of a vast chemical repertoire to find compounds with broad-spectrum potency and low toxicity. Here, we report an efficient computational method for the generation of antimicrobials with desired attributes. The method leverages guidance from classifiers trained on an informative latent space of molecules modelled using a deep generative autoencoder, and screens the generated molecules using deep-learning classifiers as well as physicochemical features derived from high-throughput molecular dynamics simulations. Within 48 days, we identified, synthesized and experimentally tested 20 candidate antimicrobial peptides, of which two displayed high potency against diverse Gram-positive and Gram-negative pathogens (including multidrug-resistant Klebsiella pneumoniae) and a low propensity to induce drug resistance in Escherichia coli. Both peptides have low toxicity, as validated in vitro and in mice. We also show using live-cell confocal imaging that the bactericidal mode of action of the peptides involves the formation of membrane pores. The combination of deep learning and molecular dynamics may accelerate the discovery of potent and selective broad-spectrum antimicrobials.