They were all products of their time, at the start of their mass killing careers firmly believing in making the world better through massive and rapid social change (Mao and Stalin believed in progressive change, Hitler was more 'regressive' although it's more complicated than that). They were inspired by Marx (yes, even Hitler) and his followers.
Hitler and Stalin resided in the same town for a while http://www.bbc.com/news/magazine-21859771