The realization that soft theorems in gauge theory and gravity are
manifestations of Ward identities for asymptotic symmetries has
reinvigorated recent attempts at flat space holography. One of the
key milestones from applying this paradigm is that it solidifies a
conjectured extension of the BMS group to include superrotations,
based on a newly discovered subleading soft graviton theorem. This
precipitated two parallel initiatives within the field. On the one
hand, the subleading soft graviton mode is a natural stress tensor
candidate for a putative dual celestial CFT with a Virasoro symmetry,
which provoked reexamining scattering amplitudes in a basis that makes
conformal covariance manifest. On the other hand, the correspondence
between the subleading soft graviton theorem and the proposed
asymptotic Virasoro superrotation symmetry does not appear to be
bijective and an extension to arbitray diffeomorphisms on the
celestial sphere was suggested. In this talk I will provide a unified
treatment of conformally soft Goldstone modes of spontaneously broken
asymptotic symmetries which will land us at the crossroads of the two
ongoing debates about what the appropriate conformal basis for
celestial CFT is and what the asymptotic symmetry group of Einstein
gravity at null infinity should be.