  In this article, we show that, for every $n \geq 2$, the pure virtual twin
group $PVT_n$ can be naturally described as a symmetric diagram group, a family
of groups introduced by V. Guba and M. Sapir and associated to semigroup
presentations. Inspired by this observation, we prove that every finitely
generated right-angled Artin group is a symmetric diagram group. This contrasts
with the fact that not all right-angled Artin groups are planar diagram groups.
