  For a finite reflection subgroup $G\leq O(n+1,1,\mR)$ of the conformal group
of the sphere with standard conformal structure $(S^n,[g_0])$, we geometrically
derive differential-difference Dunkl version of the series of conformally
invariant differential operators with symbols given by powers of Laplace
operator. The construction can be regarded as a deformation of the
Fefferman-Graham ambient metric construction of GJMS operators.
