Related papers: Technical Note on Relating Scores of Tilted Distri…
Score-based diffusion models have significantly advanced high-dimensional data generation across various domains, by learning a denoising oracle (or score) from datasets. From a Bayesian perspective, they offer a realistic modeling of data…
We introduce a new class of multivariate heavy-tailed distributions that are convolutions of heterogeneous multivariate t-distributions. Unlike commonly used heavy-tailed distributions, the multivariate convolution-t distributions embody…
Adding noise is easy; what about denoising? Diffusion is easy; what about reverting a diffusion? Diffusion-based generative models aim to denoise a Langevin diffusion chain, moving from a log-concave equilibrium measure $\nu$, say an…
Overlap, also known as positivity, is a key condition for causal treatment effect estimation. Many popular estimators suffer from high variance and become brittle when features differ strongly across treatment groups. This is especially…
A statistical mechanics theory for a fluid stratified in density is presented. The predicted statistical equilibrium state is the most probable outcome of turbulent stirring. The slow temporal evolution of the vertical density profile is…
Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential…
Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by…
It is a typical standard assumption in the density deconvolution problem that the characteristic function of the measurement error distribution is non-zero on the real line. While this condition is assumed in the majority of existing works…
Many normalizing flow architectures impose regularity constraints, yet their distributional approximation properties are not fully characterized. We study the expressivity of bi-Lipschitz normalizing flows through the lens of score-based…
Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models,…
Diffusion models have achieved remarkable success in generating samples from unknown data distributions. Most popular stochastic differential equation-based diffusion models perturb the target distribution by adding Gaussian noise,…
Score-based diffusion models have emerged as powerful tools in generative modeling, yet their theoretical foundations remain underexplored. In this work, we focus on the Wasserstein convergence analysis of score-based diffusion models.…
Consider discrete values of functions shifted by unobserved translation effects, which are independent realizations of a random variable with unknown distribution $\mu$, modeling the variability in the response of each individual. Our aim…
Score-based model research in the last few years has produced state of the art generative models by employing Gaussian denoising score-matching (DSM). However, the Gaussian noise assumption has several high-dimensional limitations,…
The paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations. High dimensionality of the data brings in many complications, such as (possibly…
Score-based diffusion models, which generate new data by learning to reverse a diffusion process that perturbs data from the target distribution into noise, have achieved remarkable success across various generative tasks. Despite their…
Diffusion models generate high-dimensional data with remarkable quality, yet how their training efficiently learns the score function, bypassing the curse of dimensionality when data is supported on low-dimensional manifolds, remains…
We establish a simple criterion for locating points where the transition density of a degenerate diffusion is strictly positive. Throughout, we assume that the diffusion satisfies a stochastic differential equation (SDE) on $\mathbf{R}^d$…
The local intrinsic dimension (LID) of data is a fundamental quantity in signal processing and learning theory, but quantifying the LID of high-dimensional, complex data has been a historically challenging task. Recent works have discovered…
Prior proposals for cumulative statistics suggest making tiny random perturbations to the scores (independent variables in a regression) in order to ensure the scores' uniqueness. Uniqueness means that no score for any member of the…