  While modern Text-to-Speech (TTS) systems can produce natural-sounding
speech, they remain unable to reproduce the full diversity found in natural
speech data. We consider the distribution of all possible real speech samples
that could be generated by these speakers alongside the distribution of all
synthetic samples that could be generated for the same set of speakers, using a
particular TTS system. We set out to quantify the distance between real and
synthetic speech via a range of utterance-level statistics related to
properties of the speaker, speech prosody and acoustic environment. Differences
in the distribution of these statistics are evaluated using the Wasserstein
distance. We reduce these distances by providing ground-truth values at
generation time, and quantify the improvements to the overall distribution
distance, approximated using an automatic speech recognition system. Our best
system achieves a 10\% reduction in distribution distance.
