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Denoising diffusion probabilistic models have been recently proposed togenerate high-quality samples by estimating the gradient of the data density.The framework defines the prior noise as a standard Gaussian distribution,whereas the corresponding data distribution may be more complicated than thestandard Gaussian distribution, which potentially introduces inefficiency indenoising the prior noise into the data sample because of the discrepancybetween the data and the prior. In this paper, we propose PriorGrad to improvethe efficiency of the conditional diffusion model for speech synthesis (forexample, a vocoder using a mel-spectrogram as the condition) by applying anadaptive prior derived from the data statistics based on the conditionalinformation. We formulate the training and sampling procedures of PriorGrad anddemonstrate the advantages of an adaptive prior through a theoretical analysis.Focusing on the speech synthesis domain, we consider the recently proposeddiffusion-based speech generative models based on both the spectral and timedomains and show that PriorGrad achieves faster convergence and inference withsuperior performance, leading to an improved perceptual quality and robustnessto a smaller network capacity, and thereby demonstrating the efficiency of adata-dependent adaptive prior.

PriorGrad: Improving Conditional Denoising Diffusion Models with Data-Dependent Adaptive Prior