  The infinite tower of positive-helicity soft gravitons in any minimally
coupled, tree-level, asymptotically flat four-dimensional (4D) gravity was
recently shown to generate a $w_{1+\infty}$ asymptotic symmetry algebra. It is
natural to ask whether this classical algebra acquires quantum corrections at
loop level. We explore this in quantum self-dual gravity, whose amplitudes
acquire known one-loop exact all-plus helicity quantum corrections. We show
using collinear splitting formulae that, remarkably, the $w_{1+\infty}$ algebra
persists in quantum self-dual gravity without corrections.
