Arbuscular mycorrhizal (AM) fungi (Glomeromycota) reproduce asexually, are multinucleate, and have high genetic variation within single cells. Pawlowska and Taylor find that genetic variation within AM fungal cells is not lost as a result of segregation, and they interpret this as evidence that the variation is present within each nucleus and that all nuclei within individual spores are genetically identical (that is, homokaryotic). Here we show that their empirical observations are also consistent with a distribution of genetic variation between nuclei within spores (that is, heterokaryotic), given that there is fusion of fungal hyphae. This analysis, together with complementary findings, suggests that AM fungi have an unusual genomic structure in which multiple, genetically diverse nuclei are maintained within cells through remixing by hyphal fusion.