Related papers: The Unreasonable Effectiveness of Gaussian Score A…

Most existing theoretical investigations of the accuracy of diffusion models, albeit significant, assume the score function has been approximated to a certain accuracy, and then use this a priori bound to control the error of generation.…

Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in Rn, the learning problem asks to estimate the means and the…

Diffusion models have been recently studied as powerful generative inverse problem solvers, owing to their high quality reconstructions and the ease of combining existing iterative solvers. However, most works focus on solving simple linear…

In the first part of this paper, we consider a family of continuous-time dynamical systems coupled with diffusion-transmutation processes. Under certain conditions, such randomly perturbed dynamical systems can be interpreted as an averaged…

Score-based model research in the last few years has produced state of the art generative models by employing Gaussian denoising score-matching (DSM). However, the Gaussian noise assumption has several high-dimensional limitations,…

Recently, conditional score-based diffusion models have gained significant attention in the field of supervised speech enhancement, yielding state-of-the-art performance. However, these methods may face challenges when generalising to…

Diffusion models have attracted a lot of attention in recent years. These models view speech generation as a continuous-time process. For efficient training, this process is typically restricted to additive Gaussian noising, which is…

This paper analyzes the convergence and generalization of training a one-hidden-layer neural network when the input features follow the Gaussian mixture model consisting of a finite number of Gaussian distributions. Assuming the labels are…

Generative diffusion models synthesize new samples by reversing a diffusive process that converts a given data set to generic noise. This is accomplished by training a neural network to match the gradient of the log of the probability…

Score-based diffusion models are a recently developed framework for posterior sampling in Bayesian inverse problems with a state-of-the-art performance for severely ill-posed problems by leveraging a powerful prior distribution learned from…

We propose closed-form conditional diffusion models for data assimilation. Diffusion models use data to learn the score function (defined as the gradient of the log-probability density of a data distribution), allowing them to generate new…

We propose a framework to perform Bayesian inference using conditional score-based diffusion models to solve a class of inverse problems in mechanics involving the inference of a specimen's spatially varying material properties from noisy…

Diffusion-based methods represented as stochastic differential equations on a continuous-time domain have recently proven successful as a non-adversarial generative model. Training such models relies on denoising score matching, which can…

While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in…

Score-based diffusion models provide a powerful way to model images using the gradient of the data distribution. Leveraging the learned score function as a prior, here we introduce a way to sample data from a conditional distribution given…

Deep neural networks (DNNs) trained for image denoising are able to generate high-quality samples with score-based reverse diffusion algorithms. These impressive capabilities seem to imply an escape from the curse of dimensionality, but…

Score matching is an approach to learning probability distributions parametrized up to a constant of proportionality (e.g. Energy-Based Models). The idea is to fit the score of the distribution, rather than the likelihood, thus avoiding the…

Diffusion models have gained traction as powerful algorithms for synthesizing high-quality images. Central to these algorithms is the diffusion process, a set of equations which maps data to noise in a way that can significantly affect…

The Gaussian graphical model is a widely used tool for learning gene regulatory networks with high-dimensional gene expression data. Most existing methods for Gaussian graphical models assume that the data are homogeneous, i.e., all samples…

Diffusion models generate samples by estimating the score function of the target distribution at various noise levels. The model is trained using samples drawn from the target distribution by progressively adding noise. Previous sample…