Related papers: Nearly $d$-Linear Convergence Bounds for Diffusion…

We consider the problem of estimating how well a model class is capable of fitting a distribution of labeled data. We show that it is often possible to accurately estimate this "learnability" even when given an amount of data that is too…

Diffusion models cannot enforce hard constraints, yet applications in the physical sciences demand exact satisfaction of conservation laws, boundary conditions, and observational consistency. In this work, we identify a corrector kernel…

Denoising diffusion models are a popular class of generative models providing state-of-the-art results in many domains. One adds gradually noise to data using a diffusion to transform the data distribution into a Gaussian distribution.…

Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…

Denoising diffusion probabilistic models (DDPMs) represent a recent advance in generative modelling that has delivered state-of-the-art results across many domains of applications. Despite their success, a rigorous theoretical understanding…

In recent years, large-scale pre-trained diffusion models have demonstrated their outstanding capabilities in image and video generation tasks. However, existing models tend to produce visual objects commonly found in the training dataset,…

We establish the O($\frac{1}{k}$) convergence rate for distributed stochastic gradient methods that operate over strongly convex costs and random networks. The considered class of methods is standard each node performs a weighted average of…

Currently, there is no general theory for deriving diffusion approximations of queueing systems with high- or infinite-dimensional state descriptors. In this paper, we explore one path for deriving diffusion limit equations of queueing…

Source localization is the inverse problem of graph information dissemination and has broad practical applications. However, the inherent intricacy and uncertainty in information dissemination pose significant challenges, and the ill-posed…

Diffusion models (DMs) have become the dominant paradigm of generative modeling in a variety of domains by learning stochastic processes from noise to data. Recently, diffusion denoising bridge models (DDBMs), a new formulation of…

We propose a unified diffusion model-based correction and super-resolution method to enhance the fidelity and resolution of diverse low-quality data through a two-step pipeline. First, the correction step employs a novel enhanced stochastic…

Discrete diffusion models have seen a surge of attention with applications on naturally discrete data such as language and graphs. Although discrete-time discrete diffusion has been established for a while, only recently Campbell et al.…

Denoising diffusion models are a class of generative models which have recently achieved state-of-the-art results across many domains. Gradual noise is added to the data using a diffusion process, which transforms the data distribution into…

We give an improved theoretical analysis of score-based generative modeling. Under a score estimate with small $L^2$ error (averaged across timesteps), we provide efficient convergence guarantees for any data distribution with second-order…

Denoising diffusion models (DDMs) offer a flexible framework for sampling from high dimensional data distributions. DDMs generate a path of probability distributions interpolating between a reference Gaussian distribution and a data…

To generate data from trained diffusion models, most inference algorithms, such as DDPM, DDIM, and other variants, rely on discretizing the reverse SDEs or their equivalent ODEs. In this paper, we view such approaches as decomposing the…

An approximate maximum likelihood method of estimation of diffusion parameters $(\vartheta,\sigma)$ based on discrete observations of a diffusion $X$ along fixed time-interval $[0,T]$ and Euler approximation of integrals is analyzed. We…

Recently, diffusion models (DMs) have made significant strides in high-quality image generation. However, the multi-step denoising process often results in considerable computational overhead, impeding deployment on resource-constrained…

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…

Learning from data in the presence of outliers is a fundamental problem in statistics. Until recently, no computationally efficient algorithms were known to compute the mean of a high dimensional distribution under natural assumptions in…