Related papers: Technical Note on Relating Scores of Tilted Distri…
Estimates of densities of convolution semigroups of probability measures are given under specific assumptions on the corresponding L\'evy measure and the L\'evy--Khinchin exponent. The assumptions are satisfied, e.g., by tempered stable…
Doubly diffusive convection is considered in a vertical slot where horizontal temperature and solutal variations provide competing effects to the fluid density while allowing the existence of a conduction state. In this configuration, the…
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…
Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…
We introduce a class of distributions originating from an exponential family and having a property related to the strict stability property. A characteristic function representation for this family is obtained and its properties are…
We study many interacting Brownian particles under a tilted periodic potential. We numerically measure the linear response coefficient of the density field by applying a slowly varying potential transversal to the tilted direction. In…
The paper studies the overdamped motion of Brownian particles in a tilted sawtooth potential. The dependencies of the diffusion coefficient and coherence level of Brownian transport on temperature, tilting force, and the shape of the…
Drifting models train one-step generators by optimizing a kernel-induced mean-shift discrepancy between the data and model distributions, with Laplace kernels used by default in practice. At each point, this discrepancy compares the…
Priors are essential for reconstructing images from noisy and/or incomplete measurements. The choice of the prior determines both the quality and uncertainty of recovered images. We propose turning score-based diffusion models into…
Solutions of the bivariate, linear errors-in-variables estimation problem with unspecified errors are expected to be invariant under interchange and scaling of the coordinates. The appealing model of normally distributed true values and…
In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the…
By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates…
We develop an analytical framework for understanding how the generated distribution evolves during diffusion model training. Leveraging a Gaussian-equivalence principle, we solve the full-batch gradient-flow dynamics of linear and…
The density estimation is one of the core problems in statistics. Despite this, existing techniques like maximum likelihood estimation are computationally inefficient due to the intractability of the normalizing constant. For this reason an…
The Collatz Conjecture's connection to dynamical systems opens it to a variety of techniques aimed at recurrence and density results. First, we turn to density results and strengthen the result of Terras through finding a strict rate of…
Score matching is a popular method for estimating unnormalized statistical models. However, it has been so far limited to simple, shallow models or low-dimensional data, due to the difficulty of computing the Hessian of log-density…
Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a…
We follow the evolution with sample thickness, of intensity statistics for localized light transmitted through layered media in a crossover from one to three dimensions occasioned by transverse disorder. The probability distribution of…
Consider the task of generating samples from a tilted distribution of a random vector whose underlying distribution is unknown, but samples from it are available. This finds applications in fields such as finance and climate science, and in…
Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…