It was Deng Xiaoping and the revolutionary but simple change he made to the standard Marxist thinking:
> Socialism means eliminating poverty. Pauperism is not socialism, still less communism. [1]
Traditionally Marxists justified the poor conditions in the socialist countries as necessary step on the road to full communism. Alternatively they blamed capitalists outside the country or some inside forces. Deng abandoned this excuse and introduced very pragmatic economic approach.
Principles like "One country, two systems" or the cat's color theory: "It doesn't matter whether a cat is black or white, as long as it catches mice." helped to push this idea trough.
Basically Chinese first moved towards Socialist market economy with limits to private ownership, but the process has taken over and it's impossible to think that private ownership would be reduced again. I don't think that new generation of leaders really want to do that. They don't believe in communist ideology anymore. They want China be like Singapore or South Korea without the democracy part.
[1]: Deng Xiaoping, BUILD SOCIALISM WITH CHINESE CHARACTERISTICS, June 30, 1984 http://academics.wellesley.edu/Polisci/wj/China/Deng/Buildin...