  Two-dimensional diffeomorphism symmetry can be described by an operator
algebra extension of the well-known Virasoro algebra description of conformal
symmetry. Utilizing this extension, this note explains why the conformal
symmetry that appears in celestial holography should not be extended to
diffeomorphism symmetry, a possibility that several authors have proposed. The
description of the two-dimensional diffeomorphism algebra presented here might
be useful for other purposes.
