How are comprehenders able to extract meaning from utterances in the presence of production errors? The noisy-channel theory provides an account grounded in Bayesian inference: comprehenders may interpret utterances non-literally in favor of an alternative with higher prior probability that is close under some error model. However, we lack implemented computational models of prior expectation and error likelihood capable of predicting human processing of arbitrary utterances. Here, we model sentence processing for noisy" utterances as incremental and approximate probabilistic inference over intended sentences and production errors. We demonstrate that the model reproduces patterns in human behavior for anomalous sentences in three separate case studies from the noisy-channel literature. Our results offer a step towards an algorithmic account of inference during real-world language comprehension. Our model code, implemented in Gen, is available at https://github.com/thomashikaru/noisy_channel_model.