Related papers: Rough path recursions and diffusion approximations

A system of interacting Brownian particles subject to short-range repulsive potentials is considered. A continuum description in the form of a nonlinear diffusion equation is derived systematically in the dilute limit using the method of…

In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…

Human motion generation is a challenging task due to its high dimensionality and the difficulty of generating fine-grained motions. Diffusion methods have been proposed due to their high sample quality and expressiveness. Early approaches…

This paper provides convergence analysis for the approximation of a class of path-dependent functionals underlying a continuous stochastic process. In the first part, given a sequence of weak convergent processes, we provide a sufficient…

In this article, we consider elliptic diffusion problems on random domains with non-smooth diffusion coefficients. We start by illustrating the problems that arise from a non-smooth diffusion coefficient by recapitulating the corresponding…

We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To…

Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…

How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that…

The iterative and stochastic nature of diffusion models enables test-time scaling, whereby spending additional compute during denoising generates higher-fidelity samples. Increasing the number of denoising steps is the primary scaling axis,…

Speech enhancement is a critical component of many user-oriented audio applications, yet current systems still suffer from distorted and unnatural outputs. While generative models have shown strong potential in speech synthesis, they are…

We consider stochastic approximations of sampling algorithms, such as Stochastic Gradient Langevin Dynamics (SGLD) and the Random Batch Method (RBM) for Interacting Particle Dynamcs (IPD). We observe that the noise introduced by the…

In this work, we consider the problem of distributed approximation of functions over multiple-access channels with additive noise. In contrast to previous works, we take fast fading into account and give explicit probability bounds for the…

Diffusion models have emerged as a powerful framework for generative tasks in deep learning. They decompose generative modeling into two computational primitives: deterministic neural-network evaluation and stochastic sampling. Current…

In the presence of quantum measurements with direct photon detection the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, from these equations one can obtain diffusion models…

This short survey article stems from recent progress on critical cases of stochastic evolution equations in variational formulation with additive, multiplicative or gradient noises. Typical examples appear as the limit cases of the…

Particle smoothing methods are used for inference of stochastic processes based on noisy observations. Typically, the estimation of the marginal posterior distribution given all observations is cumbersome and computational intensive. In…

Diffusion models have quickly become some of the most popular and powerful generative models for high-dimensional data. The key insight that enabled their development was the realization that access to the score -- the gradient of the…

We prove the path-by-path well-posedness of stochastic porous media and fast diffusion equations driven by linear, multiplicative noise. As a consequence, we obtain the existence of a random dynamical system. This solves an open problem…

Random pulse sequences are a powerful method for qubit noise spectroscopy, enabling efficient reconstruction of sparse noise spectra. Here, we advance this method in two complementary directions. First, we extend the method using a…

By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates…