Due to the absence of explicit word boundaries in the speech stream, the task of segmenting spoken sentences into word units without text supervision is particularly challenging. In this work, we leverage the most recent self-supervised speech models that have proved to quickly adapt to new tasks through fine-tuning, even in low resource conditions. Taking inspiration from semi-supervised learning, we fine-tune an XLS-R model to predict word boundaries themselves produced by top-tier speech segmentation systems: DPDP, VG-HuBERT, GradSeg and DP-Parse. Once XLS-R is fine-tuned, it is used to infer new word boundary labels that are used in turn for another fine-tuning step. Our method consistently improves the performance of each system and sets a new state-of-the-art that is, on average 130% higher than the previous one as measured by the F1 score on correctly discovered word tokens on five corpora featuring different languages. Finally, our system can segment speech from languages unseen during fine-tuning in a zero-shot fashion.