Current recommendation approaches help online merchants predict, for each visiting user, which subset of their existing products is the most relevant. However, besides being interested in matching users with existing products, merchants are also interested in understanding their users' underlying preferences. This could indeed help them produce or acquire better matching products in the future. We argue that existing recommendation models cannot directly be used to predict the optimal combination of features that will make new products serve better the needs of the target audience. To tackle this, we turn to generative models, which allow us to learn explicitly distributions over product feature combinations both in text and visual space. We develop WARHOL, a product generation and recommendation architecture that takes as input past user shopping activity and generates relevant textual and visual descriptions of novel products. We show that WARHOL can approach the performance of state-of-the-art recommendation models, while being able to generate entirely new products that are relevant to the given user profiles.