  In image compression, with recent advances in generative modeling, the
existence of a trade-off between the rate and the perceptual quality has been
brought to light, where the perception is measured by the closeness of the
output distribution to the source. This leads to the question: how does a
perception constraint impact the trade-off between the rate and traditional
distortion constraints, typically quantified by a single-letter distortion
measure? We consider the compression of a memoryless source $X$ in the presence
of memoryless side information $Z,$ studied by Wyner and Ziv, but elucidate the
impact of a perfect realism constraint, which requires the output distribution
to match the source distribution. We consider two cases: when $Z$ is available
only at the decoder or at both the encoder and the decoder. The rate-distortion
trade-off with perfect realism is characterized for sources on general
alphabets when infinite common randomness is available between the encoder and
the decoder. We show that, similarly to traditional source coding with side
information, the two cases are equivalent when $X$ and $Z$ are jointly Gaussian
under the squared error distortion measure. We also provide a general inner
bound in the case of limited common randomness.
