  Off-shell celestial amplitudes with both time-like and space-like external
legs are defined. The Feynman rules for scalar amplitudes, viewed as a set of
recursion relations for off-shell momentum space amplitudes, are transformed to
the celestial sphere using the split representation. For four-point celestial
amplitudes, the Feynman expansion is shown to be equivalent to a conformal
partial wave decomposition, providing an interpretation of conformal partial
wave expansion coefficients as integrals over off-shell three-point structures.
A conformal partial wave decomposition for a simple four-point $s$-channel
massless scalar celestial amplitude is derived.
