Generative models have been proposed as a new type of non-representational scientific models recently. A generative model is characterized with the capacity of producing new models on the basis of the existing one. The current accounts do not explain sufficiently the mechanism of the generative capacity of a generative model. I attempt to accomplish this task in this paper. I outline two antecedent accounts of generative models. I point out that both types of generative models function to generate new homogenous (...) models in the sense that the latter is a straightforward derivative of the former, both of which share many similar features. Unfortunately, both accounts are implicit about the generative capacity of generative models. Using a case study, I articulate that a two-staged process of abstraction and idealization in modeling may contribute to the generative capacity of a scientific model. I also demonstrate that this two-staged process may go beyond the capacity of generating new homogenous models to generating new heterogeneous models. (shrink)