A Comment on Loop Corrections to the Celestial Stress Tensor

In this note we show how the 1-loop exact correction to the subleading soft graviton theorem arising from IR divergences of scattering amplitudes matches onto the quadratic corrections to the soft charges computed from the BMS flux algebra. In the process, we examine how the BMS flux construction extends the celestial diamond framework to non-linear order and non-trivial vacua, and provides the natural symmetry generators for Celestial CFT.