Monolingual alignment models have been shown to boost the performance of question answering systems by "bridging the lexical chasm" between questions and answers. The main limitation of these approaches is that they require semistructured training data in the form of question-answer pairs, which is difficult to obtain in specialized domains or low-resource languages. We propose two inexpensive methods for training alignment models solely using free text, by generating artificial question-answer pairs from discourse structures. Our approach is driven by two representations of discourse: a shallow sequential representation, and a deep one based on Rhetorical Structure Theory. We evaluate the proposed model on two corpora from different genres and domains: one from Yahoo! Answers and one from the biology domain, and two types of non-factoid questions: manner and reason. We show that these alignment models trained directly from discourse structures imposed on free text improve performance considerably over an information retrieval baseline and a neural network language model trained on the same data.