We propose Future Discriminators for Generation (FUDGE), a flexible and modular method for controlled text generation. Given a pre-existing model G for generating text from a distribution of interest, FUDGE enables conditioning on a desired attribute a (for example, formality) while requiring access only to G's output logits. FUDGE learns an attribute predictor operating on a partial sequence, and uses this predictor's outputs to adjust G's original probabilities. We show that FUDGE models terms corresponding to a Bayesian decomposition of the conditional distribution of G given attribute a. Moreover, FUDGE can easily compose predictors for multiple desired attributes. We evaluate FUDGE on three tasks --- couplet completion in poetry, topic control in language generation, and formality change in machine translation --- and observe gains in all three tasks.