Evaluating and reducing the distance between synthetic and real speech distributions

While modern Text-to-Speech (TTS) systems can produce speech rated highly in terms of subjective evaluation, the distance between real and synthetic speech distributions remains understudied, where we use the term \textit{distribution} to mean the sample space of all possible real speech recordings from a given set of speakers; or of the synthetic samples that could be generated for the same set of speakers. We evaluate the distance of real and synthetic speech distributions along the dimensions of the acoustic environment, speaker characteristics and prosody using a range of speech processing measures and the respective Wasserstein distances of their distributions. We reduce these distribution distances along said dimensions by providing utterance-level information derived from the measures to the model and show they can be generated at inference time. The improvements to the dimensions translate to overall distribution distance reduction approximated using Automatic Speech Recognition (ASR) by evaluating the fitness of the synthetic data as training data.