People are capable of imagining and generating new category exemplars and categories. This ability has not been addressed by previous models of categorization, most of which focus on classifying category exemplars rather than generating them. We develop a formal account of exemplar and category generation which proposes that category knowledge is represented by probability distributions over exemplars and categories, and that new exemplars and categories are generated by sampling from these distributions. This sampling account of generation is evaluated in two pairs of behavioral experiments. In the first pair of experiments, participants were asked to generate novel exemplars of a category. In the second pair of experiments, participants were asked to generate a novel category after observing exemplars from several related categories. The results suggest that generation is influenced by both structural and distributional properties of the observed categories, and we argue that our data are better explained by the sampling account than by several alternative approaches.