Abstract: Unsupervised fact verification aims to verify a claim using evidence from a trustworthy knowledge base without any kind of data annotation. To address this challenge, algorithms must produce features for every claim that are both semantically meaningful, and compact enough to find a semantic alignment with the source information. In contrast to previous work, which tackled the alignment problem by learning over annotated corpora of claims and their corresponding labels, we propose SFAVEL ($\underline{S}$elf-supervised $\underline{Fa}$ct $\underline{Ve}$rification via $\underline{L}$anguage Model Distillation), a novel unsupervised framework that leverages pre-trained language models to distil self-supervised features into high-quality claim-evidence alignments without the need for annotations. This is enabled by a novel contrastive loss function that encourages features to attain high-quality claim and evidence alignments whilst preserving the semantic relationships across the corpora. Notably, we present results that achieve a new state-of-the-art on the standard FEVER fact verification benchmark (+8% accuracy) with linear evaluation.