AbstractAbductive and counterfactual reasoning, core abilities of everyday human cognition, require reasoning about what might have happened at time t, while conditioning on multiple contexts from the relative past and future. However, simultaneous incorporation of past and future contexts using generative language models (LMs) can be challenging, as they are trained either to condition only on the past context or to perform narrowly scoped text-infilling. In this paper, we propose DeLorean, a new unsupervised decoding algorithm that can flexibly incorporate both the past and future contexts using only off-the-shelf, left-to-right language models and no supervision. The key intuition of our algorithm is incorporating the future through back-propagation, during which, we only update the internal representation of the output while fixing the model parameters. By alternating between forward and backward propagation, DeLorean can decode the output representation that reflects both the left and right contexts. We demonstrate that our approach is general and applicable to two nonmonotonic reasoning tasks: abductive text generation and counterfactual story revision, where DeLorean outperforms a range of unsupervised and some supervised methods, based on automatic and human evaluation.