Generative models describe a class of statistical models that are a contrast to discriminative models. Informally we say that generative models can generate new data instances while discriminative models discriminate between different kinds of data instances. A generative model could generate new photos of animals that look like 'real' animals while a discriminative model could tell a dog from a cat. More formally, given a data set x and a set of labels / targets y . Generative models capture the joint probability p(x, y) , or just p(x) if there are no labels, while discriminative models capture the conditional probability p(y | x) . Discriminative models generally try to draw boundaries in the data space (often high dimensional), while generative models try to model how data is placed throughout the space.
Note: this material is thanks to Linus Ekstrøm.