Recent advances in diffusion models have positioned them as powerful generative frameworks for speech synthesis, demonstrating substantial improvements in audio quality and stability. Nevertheless, their effectiveness in vocoders conditioned on mel spectrograms remains constrained, particularly when the conditioning diverges from the training distribution. The recently proposed GLA-Grad model introduced a phase-aware extension to the WaveGrad vocoder that integrated the Griffin-Lim algorithm (GLA) into the reverse process to reduce inconsistencies between generated signals and conditioning mel spectrogram. In this paper, we further improve GLA-Grad through an innovative choice in how to apply the correction. Particularly, we compute the correction term only once, with a single application of GLA, to accelerate the generation process. Experimental results demonstrate that our method consistently outperforms the baseline models, particularly in out-of-domain scenarios.

Diffusion models are receiving a growing interest for a variety of signal generation tasks such as speech or music synthesis. WaveGrad, for example, is a successful diffusion model that conditionally uses the mel spectrogram to guide a diffusion process for the generation of high-fidelity audio. However, such models face important challenges concerning the noise diffusion process for training and inference, and they have difficulty generating high-quality speech for speakers that were not seen during training. With the aim of minimizing the conditioning error and increasing the efficiency of the noise diffusion process, we propose in this paper a new scheme called GLA-Grad, which consists in introducing a phase recovery algorithm such as the Griffin-Lim algorithm (GLA) at each step of the regular diffusion process. Furthermore, it can be directly applied to an already-trained waveform generation model, without additional training or fine-tuning. We show that our algorithm outperforms state-of-the-art diffusion models for speech generation, especially when generating speech for a previously unseen target speaker.

Denoising diffusion probabilistic models (diffusion models for short) require a large number of iterations in inference to achieve the generation quality that matches or surpasses the state-of-the-art generative models, which invariably results in slow inference speed. Previous approaches aim to optimize the choice of inference schedule over a few iterations to speed up inference. However, this results in reduced generation quality, mainly because the inference process is optimized separately, without jointly optimizing with the training process. In this paper, we propose InferGrad, a diffusion model for vocoder that incorporates inference process into training, to reduce the inference iterations while maintaining high generation quality. More specifically, during training, we generate data from random noise through a reverse process under inference schedules with a few iterations, and impose a loss to minimize the gap between the generated and ground-truth data samples. Then, unlike existing approaches, the training of InferGrad considers the inference process. The advantages of InferGrad are demonstrated through experiments on the LJSpeech dataset showing that InferGrad achieves better voice quality than the baseline WaveGrad under same conditions while maintaining the same voice quality as the baseline but with $3$x speedup ($2$ iterations for InferGrad vs $6$ iterations for WaveGrad).

This paper introduces WaveGrad, a conditional model for waveform generation which estimates gradients of the data density. The model is built on prior work on score matching and diffusion probabilistic models. It starts from a Gaussian white noise signal and iteratively refines the signal via a gradient-based sampler conditioned on the mel-spectrogram. WaveGrad offers a natural way to trade inference speed for sample quality by adjusting the number of refinement steps, and bridges the gap between non-autoregressive and autoregressive models in terms of audio quality. We find that it can generate high fidelity audio samples using as few as six iterations. Experiments reveal WaveGrad to generate high fidelity audio, outperforming adversarial non-autoregressive baselines and matching a strong likelihood-based autoregressive baseline using fewer sequential operations. Deep generative models have revolutionized speech synthesis (Oord et al., 2016; Sotelo et al., 2017; Wang et al., 2017; Biadsy et al., 2019; Jia et al., 2019; Vasquez & Lewis, 2019). Autoregressive models, in particular, have been popular for raw audio generation thanks to their tractable likelihoods, simple inference procedures, and high fidelity samples (Oord et al., 2016; Mehri et al., 2017; Kalchbrenner et al., 2018; Song et al., 2019; Valin & Skoglund, 2019). However, autoregressive models require a large number of sequential computations to generate an audio sample.