Automated program repair is the task of automatically repairing software bugs. A promising direction in this field is self-supervised learning, a learning paradigm in which repair models are trained without commits representing pairs of bug/fix. In self-supervised neural program repair, those bug/fix pairs are generated in some ways. The main problem is to generate interesting and diverse pairs that maximize the effectiveness of training. As a contribution to this problem, we propose to use back-translation, a technique coming from neural machine translation. We devise and implement MUFIN, a back-translation training technique for program repair, with specifically designed code critics to select high-quality training samples. Our results show that MUFIN's back-translation loop generates valuable training samples in a fully automated, self-supervised manner, generating more than half-a-million pairs of bug/fix. The code critic design is key because of a fundamental trade-off between how restrictive a critic is and how many samples are available for optimization during back-translation.