Reconstructing prompts that can elicit a desired answer or behaviour in an LLM is an open and important research topic. Optimisation methods which aim at minimising the perplexity of a given answer, however, consistently yield so-called pseudoprompts, unintelligible strings of tokens which can lack human interpretability. We argue that this is a consequence of the ill-posedness of the prompt optimisation task. By reframing the task as a Bayesian posterior inference over prompts, we propose an efficient algorithm to sample prompts which are both efficient (in terms of perplexity) and human readable. We compare our approach with state of the art alternatives showing on a real data set a marked improvement over a range of metrics.

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