Related papers: It\^oWave: It\^o Stochastic Differential Equation …
In this paper, we propose to unify the two aspects of voice synthesis, namely text-to-speech (TTS) and vocoder, into one framework based on a pair of forward and reverse-time linear stochastic differential equations (SDE). The solutions of…
Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting…
In this work, we propose DiffWave, a versatile diffusion probabilistic model for conditional and unconditional waveform generation. The model is non-autoregressive, and converts the white noise signal into structured waveform through a…
We consider a general one-dimensional overdamped diffusion model described by the It\^{o} stochastic differential equation (SDE) ${dX_t=\mu(X_t,t)dt+\sigma(X_t,t)dW_t}$, where $W_t$ is the standard Wiener process. We obtain a specific…
A general way of representing Stochastic Differential Equations (SDEs) on smooth manifold is based on Schwartz morphism. In this manuscript we are interested in SDEs on a smooth manifold $M$ that are driven by p-dimensional Wiener process…
We study It\^o SDE systems driven by oscillating functions of a single It\^o diffusion process. In the limit when oscillations become fast, we show that the solution process converges in law to the process defined by an SDE system driven by…
Stochastic dynamics has emerged as one of the key themes ranging from models in applications to theoretical foundations in mathematics. One class of stochastic dynamics problems that has received considerable attention recently are…
Variational autoencoders~(VAEs) have shown a promise in data-driven conversation modeling. However, most VAE conversation models match the approximate posterior distribution over the latent variables to a simple prior such as standard…
Unlike human speakers, typical text-to-speech (TTS) systems are unable to produce multiple distinct renditions of a given sentence. This has previously been addressed by adding explicit external control. In contrast, generative models are…
In this paper, we investigate the problem of string-based molecular generation via variational autoencoders (VAEs) that have served a popular generative approach for various tasks in artificial intelligence. We propose a simple, yet…
In this paper we present a new method for deriving It\^{o} stochastic delay differential equations (SDDEs) from delayed chemical master equations (DCMEs). Considering alternative formulations of SDDEs that can be derived from the same DCME,…
A new method is described for constructing a generalized solution for stochastic differential equations. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and provides a unified framework for the study of…
Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential…
We present a method for learning latent stochastic differential equations (SDEs) from high-dimensional time series data. Given a high-dimensional time series generated from a lower dimensional latent unknown It\^o process, the proposed…
This article proposes a method for forming invariant stochastic differential systems, namely dynamic systems with trajectories belonging to a given smooth manifold. The It\^o or Stratonovich stochastic differential equations with the Wiener…
Score-based (denoising diffusion) generative models have recently gained a lot of success in generating realistic and diverse data. These approaches define a forward diffusion process for transforming data to noise and generate data by…
In deep latent Gaussian models, the latent variable is generated by a time-inhomogeneous Markov chain, where at each time step we pass the current state through a parametric nonlinear map, such as a feedforward neural net, and add a small…
In this paper we present a general framework in which one can rigorously study the effect of spatio-temporal noise on traveling waves, stationary patterns and oscillations that are invariant under the action of a finite-dimensional set of…
Most state-of-the-art Text-to-Speech systems use the mel-spectrogram as an intermediate representation, to decompose the task into acoustic modelling and waveform generation. A mel-spectrogram is extracted from the waveform by a simple,…
SDE's must be solved in the "anti-Ito" sense when their coefficients are independent. While the "noise-induced drift" matters for the sample paths, it is absent in the Fokker-Planck equation, which takes a particularly simple form and is…