Lévy-Itô denoising diffusion models relying on isotropic α-stable noise instead of Gaussian distribution have recently been shown to improve performance of conventional diffusion models in image generation on imbalanced datasets while performing comparably in the standard settings. However, the stochastic algorithm of sampling from such models consists in solving the stochastic differential equation describing only an approximate inverse of the process of adding α-stable noise to data which may lead to suboptimal performance. In this paper, we derive a parametric family of stochastic differential equations whose solutions have the same marginal densities as those of the forward diffusion and show that the appropriate choice of the parameter values can improve quality of the generated images when the number of reverse diffusion steps is small. Also, we demonstrate that Lévy-Itô diffusion models are applicable to diverse domains and show that a well-trained text-to-speech Lévy-Itô model may have advantages over standard diffusion models on highly imbalanced datasets.

Diffusion models have recently become a popular generative modeling framework in various domains because of their high-quality sampling capabilities. Lately, it has been hypothesized that optimally trained diffusion models supplied with specific differential equation solvers provide a solution to the optimal transport problem between the data distribution and the prior distribution. In this paper, we empirically show that applying the optimal transport point of view on diffusion modeling allows making a good choice of a noise sample the reverse diffusion starts generating from. We consider two audio-related tasks: voice conversion and timbre transfer. In the former, we improve upon the recent state-of-the-art model and demonstrate that the optimal transport helps us to keep the prosody of the source utterances significantly better than the vanilla diffusion-based model does. As for timbre transfer, we propose the novel diffusion model capable of many-to-many timbre transfer performing on par with common algorithms in terms of the overall music quality.

Recently, denoising diffusion probabilistic models and generative score matching have shown high potential in modelling complex data distributions while stochastic calculus has provided a unified point of view on these techniques allowing for flexible inference schemes. In this paper we introduce Grad-TTS, a novel text-to-speech model with score-based decoder producing mel-spectrograms by gradually transforming noise predicted by encoder and aligned with text input by means of Monotonic Alignment Search. The framework of stochastic differential equations helps us to generalize conventional diffusion probabilistic models to the case of reconstructing data from noise with different parameters and allows to make this reconstruction flexible by explicitly controlling trade-off between sound quality and inference speed. Subjective human evaluation shows that Grad-TTS is competitive with state-of-the-art text-to-speech approaches in terms of Mean Opinion Score.

LPCNet vocoder has recently been presented to TTS community and is now gaining increasing popularity due to its effectiveness and high quality of the speech synthesized with it. In this work, we present a modification of LPCNet that is 1.5x faster, has twice less non-zero parameters and synthesizes speech of the same quality. Such enhancement is possible mostly due to two features that we introduce into the original architecture: the proposed vocoder is designed to generate 16-bit signal instead of 8-bit μ-companded signal, and it predicts two consecutive excitation values at a time independently of each other. To show that these modifications do not lead to quality degradation we train models for five different languages and perform extensive human evaluation.