Slang is a common type of informal language, but its flexible nature and paucity of data resources present challenges for existing natural language systems. We take an initial step toward machine generation of slang by developing a framework that models the speaker’s word choice in slang context. Our framework encodes novel slang meaning by relating the conventional and slang senses of a word while incorporating syntactic and contextual knowledge in slang usage. We construct the framework using a combination of probabilistic inference and neural contrastive learning. We perform rigorous evaluations on three slang dictionaries and show that our approach not only outperforms state-of-the-art language models, but also better predicts the historical emergence of slang word usages from 1960s to 2000s. We interpret the proposed models and find that the contrastively learned semantic space is sensitive to the similarities between slang and conventional senses of words. Our work creates opportunities for the automated generation and interpretation of informal language.