The production of geniuses in general seems to just be a function of the population and opportunities provided to them. The Soviet Union had a very high population — typically the 3rd highest population in the world (a distinction that went to the US, after the USSR broke up). It had an educational system that was developed in order to try and identify talent from wherever it came from and exploit that talent — it did not assume, like many places in the West did, that talent essentially ran in families. So in many ways that is a very fertile ground for cultivating genius, much more so than a country like the US where for much of the Cold War the major opportunities were reserved for white men exclusively.

But obviously the Soviet Union had its downsides as well. It was an oppressive political system, and any opportunities for advancement had to come through the state, not engines of private development that have historically driven a lot of technological and scientific innovation. So there were real limitations on the kinds of advancements they made (what domains they were in, for example — not biology, which was crippled by political decisions), and it was as you imagine not always the place that intellectuals and scientists wanted to live. Many Soviet-born-and-educated scientists did want to leave the country, but as you probably know it was made quite difficult to do so for much of its history. For a prominent scientist, it was uncommon to let them and their spouse both leave for a conference at the same time, because of the fear that both would abscond. Such people were often given "minders" when they went abroad; KGB agents whose job it was was to keep an eye on them.

That being said, many of said scientists were treated much better than the average Soviet citizen. The rewards could be high and so could their relative freedom to dissent or criticize; if they were sufficiently prominent internationally, it gave them some "buffer" against those forces. But it was always limited.

The historian of Soviet and Russian science, Loren Graham, asked at the end of the Cold War what the history of the Soviet scientific experience told us. One of the conclusions he came to was that if you wanted to have scientific and technical advancement, funding was more important than freedom: the Russian state in the immediate post-Cold War could not maintain the same level of funding as the Soviet state had, and its scientific contributions immediately withered. It is an interesting question to ask, given that in the Western context we frequently focus on freedom as the prerequisite for such work, but the data doesn't totally bear that out (though obviously there are limits: it is clear that scientific work does not flourish in areas where state interference deliberately suppresses it, as in the case of biology in the USSR).

It is easy to forget this now, but for much of the Cold War there was active debate about what the best "model" for science was, and the Soviet model seemed to many to be a superior one: the state would directly fund scientific work that it thought was important, as opposed to either a model where most funding came from the private sector, or the sort of hybrid model that the US ended up developing in the wake of World War II (the NSF/military model is sort of a mixed model). Today we tend to see the inefficiencies of the Soviet model, as we do with all aspects of the failed Soviet state. But there are, of course, inefficiencies in the American model as well, if one cares to look for them.

The Graham book I mentioned is Loren R. Graham, What Have We Learned About Science and Technology from the Russian Experience? (Stanford University Press, 1998). Graham's _ Science in Russia and the Soviet Union: A Short History_ (Cambridge University Press, 1994) is a great overview of the development of Soviet science, its pros and its cons.