Maximum a posteriori decoding, a commonly used method for neural machine translation (NMT), aims to maximize the estimated posterior probability. However, high estimated probability does not always lead to high translation quality. Minimum Bayes Risk (MBR) decoding (\citealp{kumar2004minimum}) offers an alternative by seeking hypotheses with the highest expected utility. Inspired by Quality Estimation (QE) reranking which uses the QE model as a ranker (\citealp{fernandes-etal-2022-quality}), we propose source-based MBR (sMBR) decoding, a novel approach that utilizes quasi-sources (generated via paraphrasing or back-translation) as ``support hypotheses'' and a reference-free quality estimation metric as the utility function, marking the first work to solely use sources in MBR decoding. Experiments show that sMBR outperforms QE reranking and the standard MBR decoding. Our findings suggest that sMBR is a promising approach for NMT decoding.

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