One way to stabilize world population is to reduce the birthrate via better birth control and more liberal attitudes about sexual alternatives.
Another way is for the death rate to increase from famine, war, poverty and even genocide. The first way is more desirable.
Even a small amount of population growth could possibly still happen if our consumption of resources were sustainable for climate stability and so forth. This can be achieved with technological innovation as well as the type of economics that would promote less consumption. Quality of life can, conceivably, improve; depending on how people define quality of life.
A good question to ask, worldwide, is whether humanity has the political will to develop a sustainable world.