Facilitated diffusion does not require energy. Facilitated diffusion describes the process by which solutes are carried across cell membranes by proteins. Another process that does the same thing is called active transport; active transport does require a form of chemical energy.
Facilitated diffusion occurs when a solute moves from an area of higher concentration across a cell membrane to an area of lower concentration. The move is referred to as a "downhill" move. Facilitated diffusion is used by red blood cells to move glucose over membranes; facilitated diffusion works in this instance due to the stability of glucose levels in blood and the fact that cellular concentration is generally lower than glucose concentration.