Related papers: Diffusion models with location-scale noise

Diffusion-based generative models have recently gained attention in speech enhancement (SE), providing an alternative to conventional supervised methods. These models transform clean speech training samples into Gaussian noise centered at…

An elementary approach to characterizing the impact of noise scheduling and time discretization in generative diffusion models is developed. We first utilize the Cram\'er-Rao bound to identify the Gaussian setting as a fundamental…

We give a new algorithm for learning mixtures of $k$ Gaussians (with identity covariance in $\mathbb{R}^n$) to TV error $\varepsilon$, with quasi-polynomial ($O(n^{\text{poly\,log}\left(\frac{n+k}{\varepsilon}\right)})$) time and sample…

The goal of speech enhancement (SE) is to eliminate the background interference from the noisy speech signal. Generative models such as diffusion models (DM) have been applied to the task of SE because of better generalization in unseen…

Diffusion models have demonstrated powerful performance in generating high-quality images. A typical example is text-to-image generator like Stable Diffusion. However, their widespread use also poses potential privacy risks. A key concern…

Exploring noise distributions beyond Gaussian in diffusion models remains an open challenge. While Gaussian-based models succeed within a unified SDE framework, recent studies suggest that heavy-tailed noise distributions, like…

Beyond estimating parameters of interest from data, one of the key goals of statistical inference is to properly quantify uncertainty in these estimates. In Bayesian inference, this uncertainty is provided by the posterior distribution, the…

Diffusion models achieve state-of-the-art image generation but remain computationally costly due to iterative denoising. Latent-space models like Stable Diffusion reduce overhead yet lose fine detail, while retrieval-augmented methods…

3D Gaussian Splatting (3DGS) has become a powerful representation for image-based object reconstruction, yet its performance drops sharply in sparse-view settings. Prior works address this limitation by employing diffusion models to repair…

We introduce a Cascaded Diffusion Model (Cas-DM) that improves a Denoising Diffusion Probabilistic Model (DDPM) by effectively incorporating additional metric functions in training. Metric functions such as the LPIPS loss have been proven…

The non-Gaussian normal diffusion, i.e., the probability distribution function (PDF) is non-Gaussian but the mean squared displacement (MSD) depends on time linearly, has been observed in particle motions. Here we show by numerical…

We propose a novel diffusion map particle system (DMPS) for generative modeling, based on diffusion maps and Laplacian-adjusted Wasserstein gradient descent (LAWGD). Diffusion maps are used to approximate the generator of the corresponding…

Recent advances in text-to-image diffusion models have been driven by the increasing availability of paired 2D data. However, the development of 3D diffusion models has been hindered by the scarcity of high-quality 3D data, resulting in…

Diffusion models (DMs) have become dominant in visual generation but suffer performance drop when tested on resolutions that differ from the training scale, whether lower or higher. In fact, the key challenge in generating variable-scale…

Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…

Generative Artificial Intelligence (GenAI) models, with their powerful feature learning capabilities, have been applied in many fields. In mobile wireless communications, GenAI can dynamically optimize the network to enhance the user…

Diffusion models are a class of generative models that have demonstrated remarkable success in tasks such as image generation. However, one of the bottlenecks of these models is slow sampling due to the delay before the onset of trajectory…

The purpose of this paper is to provide a discussion, with illustrating examples, on Bayesian forecasting for dynamic generalized linear models (DGLMs). Adopting approximate Bayesian analysis, based on conjugate forms and on Bayes linear…

Denoising diffusion models have proven to be a flexible and effective paradigm for generative modelling. Their recent extension to infinite dimensional Euclidean spaces has allowed for the modelling of stochastic processes. However, many…

Conditional diffusion models have achieved remarkable success in various generative tasks recently, but their training typically relies on large-scale datasets that inevitably contain imprecise information in conditional inputs. Such…