A great deal of the money trickles down from the Olympics/IOC (WADA).
Individual sporting bodies are also under a great deal of pressure to comply with WADA standards, since there is a very real threat of being kicked out of the Olympics for insufficiently draconian enforcement (a perennial story with Weightlifting / IWF). So in many cases the athletes themselves pay for it via their dues to their sporting body.
Who pays for all this anti-doping bureaucracy? It sounds very expensive for both the agency and the athletes.