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Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…

We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…

For object detection, it is possible to view the prediction of bounding boxes as a reverse diffusion process. Using a diffusion model, the random bounding boxes are iteratively refined in a denoising step, conditioned on the image. We…

Remote sensing change detection is crucial for understanding the dynamics of our planet's surface, facilitating the monitoring of environmental changes, evaluating human impact, predicting future trends, and supporting decision-making. In…

Big data often has emergent structure that exists at multiple levels of abstraction, which are useful for characterizing complex interactions and dynamics of the observations. Here, we consider multiple levels of abstraction via a…

Based on the Denoising Diffusion Probabilistic Model (DDPM), medical image segmentation can be described as a conditional image generation task, which allows to compute pixel-wise uncertainty maps of the segmentation and allows an implicit…

Diffusion models benefit from instillation of task-specific information into the score function to steer the sample generation towards desired properties. Such information is coined as guidance. For example, in text-to-image synthesis, text…

The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…

In this paper, we develop a novel high-dimensional time-varying coefficient estimation method, based on high-dimensional It\^o diffusion processes. To account for high-dimensional time-varying coefficients, we first estimate local (or…

This paper investigates score-based diffusion models when the underlying target distribution is concentrated on or near low-dimensional manifolds within the higher-dimensional space in which they formally reside, a common characteristic of…

Medical imaging often contains critical fine-grained features, such as tumors or hemorrhages, crucial for diagnosis yet potentially too subtle for detection with conventional methods. In this paper, we introduce \textit{DIA}, dissolving is…

We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…

Diffusion models have revolutionized image generation in recent years, yet they are still limited to a few sizes and aspect ratios. We propose ElasticDiffusion, a novel training-free decoding method that enables pretrained text-to-image…

Self-diffusion coefficients, $D^*$, are routinely estimated from molecular dynamics simulations by fitting a linear model to the observed mean-squared displacements (MSDs) of mobile species. MSDs derived from simulation exhibit statistical…

We present an approach to deep estimation of discrete conditional probability distributions. Such models have several applications, including generative modeling of audio, image, and video data. Our approach combines two main techniques:…

The Single Ion Differential alpha Measurement (SIDAM) method for measuring fine stucture variations (daa)and its figures of merit are illustrated together with the results produced by means of FeII absorption lines of QSO intervening…

Conditioning, the central operation in Bayesian statistics, is formalised by the notion of disintegration of measures. However, due to the implicit nature of their definition, constructing disintegrations is often difficult. A folklore…

Surface anomaly detection is a vital component in manufacturing inspection. Current discriminative methods follow a two-stage architecture composed of a reconstructive network followed by a discriminative network that relies on the…

We report on measurements of self-diffusion coefficients in discrete numerical simulations of steady, homogeneous, collisional shearing flows of nearly identical, frictional, inelastic spheres. We focus on a range of relatively high solid…

Accurate image segmentation remains challenging, particularly in generating sharp, confident boundaries. While modern architectures have advanced the field, many of them still rely on standard loss functions like Cross-Entropy and Dice,…