Why does heated air rise in colder air?

This phenomenon can be explained as follows: cold air, by itself, is heavier than warm air. Due to the fact that the air is warm, there is a rapid movement of molecules. Because of this, the density is violated, the air itself becomes less dense in comparison with cold air. That is why the buoyancy force from the cold air acts on warm air. As a result, warm air rises in cold air.