Related papers: When Diffusion Model Can Ignore Dimension: An Entr…

Score-based diffusion models are a powerful class of generative models, but their practical use often depends on training neural networks to approximate the score function. Training-free diffusion models provide an attractive alternative by…

The manifold hypothesis asserts that data of interest in high-dimensional ambient spaces, such as image data, lies on unknown low-dimensional submanifolds. Diffusion models (DMs) -- which operate by convolving data with progressively larger…

Diffusion models accomplish remarkable success in data generation tasks across various domains. However, the iterative sampling process is computationally expensive. Consistency models are proposed to learn consistency functions to map from…

Image restoration, which aims to recover high-quality images from their corrupted counterparts, often faces the challenge of being an ill-posed problem that allows multiple solutions for a single input. However, most deep learning based…

Despite achieving promising results in a breadth of medical image segmentation tasks, deep neural networks require large training datasets with pixel-wise annotations. Obtaining these curated datasets is a cumbersome process which limits…

Mixture distributions are a workhorse model for multimodal data in information theory, signal processing, and machine learning. Yet even when each component density is simple, the differential entropy of the mixture is notoriously hard to…

Diffusion models have found valuable applications in anomaly detection by capturing the nominal data distribution and identifying anomalies via reconstruction. Despite their merits, they struggle to localize anomalies of varying scales,…

An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed…

Denoising diffusion models are a recent class of generative models exhibiting state-of-the-art performance in image and audio synthesis. Such models approximate the time-reversal of a forward noising process from a target distribution to a…

Diffusion models have been successfully adapted to text generation tasks by mapping the discrete text into the continuous space. However, there exist nonnegligible gaps between training and inference, owing to the absence of the forward…

Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…

Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…

Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…

Information has an entropic character which can be analyzed within the Statistical Theory in molecular systems. R. Landauer and C.H. Bennett showed that a logical copy can be carried out in the limit of no dissipation if the computation is…

Diffusion-based generative models are extremely effective in generating high-quality images, with generated samples often surpassing the quality of those produced by other models under several metrics. One distinguishing feature of these…

We study the memorization and generalization capabilities of Diffusion Models (DMs) when data lies on a structured latent manifold. Specifically, we consider a set of $P$ data points in $N$ dimensions confined to a latent subspace of…

Diffusion models have excellent capacity to model complex distributions of natural data, which has made them a popular and effective choice for posterior sampling in imaging inverse problems. Existing methods can incorporate any measurement…

Discrete flow models (DFMs) have been proposed to learn the data distribution on finite state space, offering a flexible framework as an alternative to discrete diffusion models. A line of recent work has studied samplers for discrete…

Accelerated diffusion models hold the potential to significantly enhance the efficiency of standard diffusion processes. Theoretically, these models have been shown to achieve faster convergence rates than the standard $\mathcal…

In recent deep image compression neural networks, the entropy model plays a critical role in estimating the prior distribution of deep image encodings. Existing methods combine hyperprior with local context in the entropy estimation…