After the destruction of Torna and its Kingdom by Amalthus and the Indoline Praetorium's warriors, the survivors fled to Genbu and created the Kingdom of Tantal. This Kingdom was led by one of the cadet branch of the Tornan royal Family, the Tantalese royal family soon revendicated Addam Origo's bloodline as a mean to prevent civil war even if that was a lie. Amalthus knew that and forced Tantal to give a fixed quantity of Core Chips each year in exchange of his silence, this destroyed Genbu's climate and the Tantalese were soon condemned to live in a perpetual winter. The royal family decided to turn Tantal into an isolationist state by sinking the Titan in the Cloud Sea and have Pandoria as one of the only mean to have him come to the surface, the other being the Omega Fetter.
During Xenoblade Chronicles 2
When the ether accelerator is fired at Pyra, the Omega Fetter goes out of control and Genbu begins to dive beneath the Cloud Sea, threatening to crush itself and everyone within it with the pressure. The party eventually travels to its head, where they find the Omega Fetter in an unstable state. Mythra is able to repair the crystal, and Pandoria tells Genbu to rise back up out of the Cloud Sea.
In the English version, the Japanese name "Genbu", or "Xuánwǔ" (玄武) in Chinese, is the Black Tortoise in the Chinese constellations. It is one of the four symbols and represents the north and the winter season which fits with Genbu's climate and appearance.
In the Japanese version, the name "Luxuria" alludes to one of the seven deadly sins found in the Christian religion, lust.