Increases in biodiversity often lead to greater, and less variable, levels of ecosystem functioning. However, whether species are less likely to go extinct in more diverse ecosystems is unclear. We use comprehensive estimates of avian taxonomic, phylogenetic and functional diversity to characterise the global relationship between multiple dimensions of diversity and extinction risk in birds, focusing on contemporary threat status and latent extinction risk. We find that more diverse assemblages have lower mean IUCN threat status despite being composed of species with attributes that make them more vulnerable to extinction, such as large body size or small range size. Indeed, the reduction in current threat status associated with greater diversity far outweighs the increased risk associated with the accumulation of extinction-prone species in more diverse assemblages. Our results suggest that high diversity reduces extinction risk, and that species conservation targets may therefore best be achieved by maintaining high levels of overall biodiversity in natural ecosystems.