  We study the dynamic scaling hypothesis in invariant surface growth. We show
that the existence of power-law scaling of the correlation functions (scale
invariance) does not determine a unique dynamic scaling form of the correlation
functions, which leads to the different anomalous forms of scaling recently
observed in growth models. We derive all the existing forms of anomalous
dynamic scaling from a new generic scaling ansatz. The different scaling forms
are subclasses of this generic scaling ansatz associated with bounds on the
roughness exponent values. The existence of a new class of anomalous dynamic
scaling is predicted and compared with simulations.
