late 14c., "an overflowing of water, a great flood, Noah's Flood in Genesis," from Old French deluge (12c.), earlier deluve, from Latin diluvium "flood, inundation," from diluere "wash away," from dis- "away" (see dis-) + -luere, combining form of lavere "to wash" (from PIE root *leue- "to wash"). Figurative sense of "anything that overflows or floods" is from early 15c.
After me the deluge (F. après moi le déluge), a saying ascribed to Louis XV, who expressed thus his indifference to the results of his policy of selfish and reckless extravagance, and perhaps his apprehension of coming disaster. [Century Dictionary]
1590s, "to pour over, overwhelm in a flood, inundate;" see deluge (n.). Figurative sense of "overrun like a flood, pour over in overwhelming numbers" is from 1650s. Related: Deluged; deluging.