In this paper we study semi-group generation by semi-bounded second order differential operators on a noncompact $C^\infty $ manifold. It is shown that the usual regularity assumptions can be relaxed to include hypoelliptic operators of the Hormander type. The related question of the identity between weak and strong extensions for such operators is also studied. Sufficient conditions are given in terms of the behavior at infinity of an appropriate exhaustion function. We include examples to illustrate how this function may be chosen in concrete applications.