  Denoising diffusion probabilistic models (DDPMs) have recently achieved
leading performances in many generative tasks. However, the inherited iterative
sampling process costs hindered their applications to speech synthesis. This
paper proposes FastDiff, a fast conditional diffusion model for high-quality
speech synthesis. FastDiff employs a stack of time-aware location-variable
convolutions of diverse receptive field patterns to efficiently model long-term
time dependencies with adaptive conditions. A noise schedule predictor is also
adopted to reduce the sampling steps without sacrificing the generation
quality. Based on FastDiff, we design an end-to-end text-to-speech synthesizer,
FastDiff-TTS, which generates high-fidelity speech waveforms without any
intermediate feature (e.g., Mel-spectrogram). Our evaluation of FastDiff
demonstrates the state-of-the-art results with higher-quality (MOS 4.28) speech
samples. Also, FastDiff enables a sampling speed of 58x faster than real-time
on a V100 GPU, making diffusion models practically applicable to speech
synthesis deployment for the first time. We further show that FastDiff
generalized well to the mel-spectrogram inversion of unseen speakers, and
FastDiff-TTS outperformed other competing methods in end-to-end text-to-speech
synthesis. Audio samples are available at \url{https://FastDiff.github.io/}.
