  We study solutions to generalized Ricci flow on four-manifolds with a
nilpotent, codimension $1$ symmetry. We show that all such flows are immortal,
and satisfy type III curvature and diameter estimates. Using a new kind of
monotone energy adapted to this setting, we show that blowdown limits lie in a
canonical finite-dimensional family of solutions. The results are new for Ricci
flow.
