Error Span Detection (ESD) is a crucial subtask in Machine Translation (MT) evaluation, aiming to identify the location and severity of translation errors. While fine-tuning models on human-annotated data improves ESD performance, acquiring such data is expensive and prone to inconsistencies among annotators. To address this, we propose a novel self-evolution framework based on Minimum Bayes Risk (MBR) decoding, named Iterative MBR Distillation for ESD, which eliminates the reliance on human annotations by leveraging an off-the-shelf LLM to generate pseudo-labels. Extensive experiments on the WMT Metrics Shared Task datasets demonstrate that models trained solely on these self-generated pseudo-labels outperform both unadapted base model and supervised baselines trained on human annotations at the system and span levels, while maintaining competitive sentence-level performance.

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 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, 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.