The deep ocean is the largest and least-explored ecosystem on Earth, and a uniquely energy-poor environment. The distribution, drivers and origins of deep-sea biodiversity remain unknown at global scales. Here we analyse a database of more than 165,000 distribution records of Ophiuroidea (brittle stars), a dominant component of sea-floor fauna, and find patterns of biodiversity unlike known terrestrial or coastal marine realms. Both patterns and environmental predictors of deep-sea (2,000-6,500 m) species richness fundamentally differ from those found in coastal (0-20 m), continental shelf (20-200 m), and upper-slope (200-2,000 m) waters. Continental shelf to upper-slope richness consistently peaks in tropical Indo-west Pacific and Caribbean (0-30°) latitudes, and is well explained by variations in water temperature. In contrast, deep-sea species show maximum richness at higher latitudes (30-50°), concentrated in areas of high carbon export flux and regions close to continental margins. We reconcile this structuring of oceanic biodiversity using a species-energy framework, with kinetic energy predicting shallow-water richness, while chemical energy (export productivity) and proximity to slope habitats drive deep-sea diversity. Our findings provide a global baseline for conservation efforts across the sea floor, and demonstrate that deep-sea ecosystems show a biodiversity pattern consistent with ecological theory, despite being different from other planetary-scale habitats.