Precise doping-profile engineering in van der Waals heterostructures is a key element to promote optimal device performance in various electrical and optical applications with two-dimensional layered materials. Here, we report tungsten diselenide- (WSe2) based pure vertical diodes with atomically defined p-, i- and n-channel regions. Externally modulated p- and n-doped layers are respectively formed on the bottom and the top facets of WSe2 single crystals by direct evaporations of high and low work-function metals platinum and gadolinium, thus forming atomically sharp p-i-n heterojunctions in the homogeneous WSe2 layers. As the number of layers increases, charge transport through the vertical WSe2 p-i-n heterojunctions is characterized by a series of quantum tunneling events; direct tunneling, Fowler-Nordheim tunneling, and Schottky emission tunneling. With optimally selected WSe2 thickness, our vertical heterojunctions show superb diode characteristics of an unprecedentedly high current density and low turn-on voltages while maintaining good current rectification.