I'm aware that every topological group is uniformizable: given a neighborhood $U\in\mathcal N(e)$ of the identity, the set $D_U=\{\langle x,y\rangle:x^{-1}y\in U\text{ and }xy^{-1}\in U\}$ is an entourage of the diagonal and $\mathbb D=\{D_U:U\in\mathcal N(e)\}$ is a base for a uniformity compatible with the topology.
Is this $\mathbb D$ a base for the universal/fine uniformity (the union of all compatible uniformities) on a topological group? If not, when is it? And if not, is there a similar algebraic characterization of the universal/fine uniformity?