Over the past decade, the illicit drug market has been reshaped by the proliferation of clandestinely produced designer drugs. These agents, referred to as new psychoactive substances (NPSs), are designed to mimic the physiological actions of better-known drugs of abuse while skirting drug control laws. The public health burden of NPS abuse obliges toxicological, police and customs laboratories to screen for them in law enforcement seizures and biological samples. However, the identification of emerging NPSs is challenging due to the chemical diversity of these substances and the fleeting nature of their appearance on the illicit market. Here we present DarkNPS, a deep learning-enabled approach to automatically elucidate the structures of unidentified designer drugs using only mass spectrometric data. Our method employs a deep generative model to learn a statistical probability distribution over unobserved structures, which we term the structural prior. We show that the structural prior allows DarkNPS to elucidate the exact chemical structure of an unidentified NPS with an accuracy of 51% and a top-10 accuracy of 86%. Our generative approach has the potential to enable de novo structure elucidation for other types of small molecules that are routinely analysed by mass spectrometry.