Speaking in Wavelet Domain: A Simple and Efficient Approach to Speed up Speech Diffusion Model

Recently, Denoising Diffusion Probabilistic Models (DDPMs) have attained leading performances across a diverse range of generative tasks. However, in the field of speech synthesis, although DDPMs exhibit impressive performance, their long training duration and substantial inference costs hinder practical deployment. Existing approaches primarily focus on enhancing inference speed, while approaches to accelerate training a key factor in the costs associated with adding or customizing voices often necessitate complex modifications to the model, compromising their universal applicability. To address the aforementioned challenges, we propose an inquiry: is it possible to enhance the training/inference speed and performance of DDPMs by modifying the speech signal itself? In this paper, we double the training and inference speed of Speech DDPMs by simply redirecting the generative target to the wavelet domain. This method not only achieves comparable or superior performance to the original model in speech synthesis tasks but also demonstrates its versatility. By investigating and utilizing different wavelet bases, our approach proves effective not just in speech synthesis, but also in speech enhancement.