We've already revealed that the KGB helped disseminate the Kennedy assassination conspiracy theory long before Oliver Stone. And in 1992, former Russian intelligence chief / Prime Minister Yevgeni Primakov admitted that they had also manufactured the idea that AIDS was developed by the US military -- a theory which it seems was too nutty for even Oliver Stone to bother with.
Because they also apparently had a good eye for marketing and the importance of branding, the Soviets dubbed their campaign "Operation INFEKTION." They started by planting suggestions that AIDS outbreaks in various countries were the result of U.S. biological weapons testing in worldwide media that they secretly controlled, such as newspapers, radio broadcasts, and even pornography (evidently to catch that demographic that doesn't read newspapers). Then the Russians published even more articles that referenced the original misinformation to create the illusion that this was all totally well-sourced.
Eventually, East German biophysicist Jakob Segal fell for the hoax, and began publishing his own in-depth articles about how the American government had totally engineered AIDS. Segal claimed that the CIA paid him a visit and threatened him to keep his mouth shut. This seems unlikely, considering how nothing he was writing was true, so either he made the meeting up out of whole cloth or the "CIA agents" were KGB agents in disguise working a kind of reverse psychology. In any case, it worked: Segal's impressive credentials gave the theory the legitimacy it needed, and the conspiracy theory finally blew up.
However, when AIDS inevitably spread to Russia, Soviet scientists were forced to consult with American researchers on how to fight and contain the disease. The whole "AIDS was engineered by America" thing made cooperation a little awkward, so the Russian media took a 180-degree turn on the issue and began loudly discrediting the US-AIDS connection they had spent so much time and energy creating. Unfortunately, like any good rumor, the story was well out of the KGB's hands by this point, and the idea persists to this day. (Note: You cannot kill a good conspiracy theory.)