  Denoising diffusion probabilistic models (DDPMs) have recently achieved
leading performances in many generative tasks. However, the inherited iterative
sampling process costs hinder their applications to text-to-speech deployment.
Through the preliminary study on diffusion model parameterization, we find that
previous gradient-based TTS models require hundreds or thousands of iterations
to guarantee high sample quality, which poses a challenge for accelerating
sampling. In this work, we propose ProDiff, on progressive fast diffusion model
for high-quality text-to-speech. Unlike previous work estimating the gradient
for data density, ProDiff parameterizes the denoising model by directly
predicting clean data to avoid distinct quality degradation in accelerating
sampling. To tackle the model convergence challenge with decreased diffusion
iterations, ProDiff reduces the data variance in the target site via knowledge
distillation. Specifically, the denoising model uses the generated
mel-spectrogram from an N-step DDIM teacher as the training target and distills
the behavior into a new model with N/2 steps. As such, it allows the TTS model
to make sharp predictions and further reduces the sampling time by orders of
magnitude. Our evaluation demonstrates that ProDiff needs only 2 iterations to
synthesize high-fidelity mel-spectrograms, while it maintains sample quality
and diversity competitive with state-of-the-art models using hundreds of steps.
ProDiff enables a sampling speed of 24x faster than real-time on a single
NVIDIA 2080Ti GPU, making diffusion models practically applicable to
text-to-speech synthesis deployment for the first time. Our extensive ablation
studies demonstrate that each design in ProDiff is effective, and we further
show that ProDiff can be easily extended to the multi-speaker setting. Audio
samples are available at \url{https://ProDiff.github.io/.}
