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.

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