Related papers: Product of Gaussian Mixture Diffusion Models
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…
While diffusion models have shown great success in image generation, their noise-inverting generative process does not explicitly consider the structure of images, such as their inherent multi-scale nature. Inspired by diffusion models and…
Diffusion models (DMs) are generative models that learn to synthesize images from Gaussian noise. DMs can be trained to do a variety of tasks such as image generation and image super-resolution. Researchers have made significant…
Conditional diffusion probabilistic models can model the distribution of natural images and can generate diverse and realistic samples based on given conditions. However, oftentimes their results can be unrealistic with observable color…
The Dirichlet process mixture model and more general mixtures based on discrete random probability measures have been shown to be flexible and accurate models for density estimation and clustering. The goal of this paper is to illustrate…
We consider the problem of estimating the conditional probability distribution of missing values given the observed ones. We propose an approach, which combines the flexibility of deep neural networks with the simplicity of Gaussian mixture…
We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac…
Suppose X is a multivariate diffusion process that is observed discretely in time. At each observation time, a transformation of the state of the process is observed with noise. The smoothing problem consists of recovering the path of the…
Standard diffusion models involve an image transform -- adding Gaussian noise -- and an image restoration operator that inverts this degradation. We observe that the generative behavior of diffusion models is not strongly dependent on the…
The gradient discretisation method (GDM) is a generic framework for designing and analysing numerical schemes for diffusion models. In this paper, we study the GDM for the porous medium equation, including fast diffusion and slow diffusion…
Multivariate density estimation and graphical models play important roles in statistical learning. The estimated density can be used to construct a graphical model that reveals conditional relationships whereas a graphical structure can be…
Along with recent diffusion models, randomized smoothing has become one of a few tangible approaches that offers adversarial robustness to models at scale, e.g., those of large pre-trained models. Specifically, one can perform randomized…
Real-world image denoising is an extremely important image processing problem, which aims to recover clean images from noisy images captured in natural environments. In recent years, diffusion models have achieved very promising results in…
Image deblurring is an ill-posed problem with multiple plausible solutions for a given input image. However, most existing methods produce a deterministic estimate of the clean image and are trained to minimize pixel-level distortion. These…
Assuming that a stochastic process $X=(X_t)_{t\geq 0}$ is a sum of a compound Poisson process $Y=(Y_t)_{t\geq 0}$ with known intensity $\lambda$ and unknown jump size density $f,$ and an independent Brownian motion $Z=(Z_t)_{t\geq 0},$ we…
Recently, diffusion models have shown remarkable results in image synthesis by gradually removing noise and amplifying signals. Although the simple generative process surprisingly works well, is this the best way to generate image data? For…
The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into…
Diffusion models have attained remarkable success in the domains of image generation and editing. It is widely recognized that employing larger inversion and denoising steps in diffusion model leads to improved image reconstruction quality.…
Computing sample means on Riemannian manifolds is typically computationally costly as exemplified by computation of the Fr\'echet mean which often requires finding minimizing geodesics to each data point for each step of an iterative…
Conditional Density Estimation (CDE) models deal with estimating conditional distributions. The conditions imposed on the distribution are the inputs of the model. CDE is a challenging task as there is a fundamental trade-off between model…