WaveGrad: Estimating Gradients for Waveform Generation

Abstract

This paper introduces WaveGrad, a conditional model for waveform generation through estimating gradients of the data density. This model is built on the prior work on score matching and diffusion probabilistic models. It starts from Gaussian white noise and iteratively refines the signal via a gradient-based sampler conditioned on the mel-spectrogram. WaveGrad is non-autoregressive, and requires only a constant number of generation steps during inference. It can use as few as 6 iterations to generate high fidelity audio samples. WaveGrad is simple to train, and implicitly optimizes for the weighted variational lower-bound of the log-likelihood. Empirical experiments reveal WaveGrad to generate high fidelity audio samples matching a strong likelihood-based autoregressive baseline with less sequential operations. * Work done during an internship at Google Brain. † Equal contribution.

DiffuseMorph: Unsupervised Deformable Image Registration Along Continuous Trajectory Using Diffusion Models

“…x 0 = f . Moreover, to make the network G θ aware of the level of noise, we directly give the adequate statistics for the variance of the noise α to the network, similar to [8,34].…”

“…where z ∼ N (0, I). Here, in choosing the total sampling steps T , we employ [8] that presents a more efficient inference method than DDPM. Due to the directly conditioning our denoising model on the noise level α, one can flexibly set the number of sampling steps.…”

“…Recently, the denoising diffusion probabilistic model (DDPM) [18,36] has shown impressive performance in many areas of computer vision [8,15,21,35,37]. DDPM learns the Markov transformation from Gaussian noise distribution to data distribution and provides diverse samples through stochastic diffusion processes.…”

Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models

“…We show results under trajectories of different number of timesteps K. We select the minimum K such that analytic-DPM can outperform the baselines with full timesteps and underline the corresponding results. (Chen et al, 2020;Kong et al, 2020;Popov et al, 2021;Lam et al, 2021), controllable generation (Choi et al, 2021;Sinha et al, 2021), image super-resolution (Saharia et al, 2021;, image-to-image translation (Sasaki et al, 2021), shape generation (Zhou et al, 2021) and time series forecasting (Rasul et al, 2021).…”

“…It would be interesting to apply Analytic-DPM to other data modalities, e.g. speech data (Chen et al, 2020). As presented in Appendix E, our method can be applied to continuous DPMs, e.g., variational diffusion models (Kingma et al, 2021) that learn the forward noise schedule.…”