相关论文: Diffusion Mean Estimation on the Diagonal of Produ…

Diffusion models may be viewed as hierarchical variational autoencoders (VAEs) with two improvements: parameter sharing for the conditional distributions in the generative process and efficient computation of the loss as independent terms…

Motivated by the problem of nonparametric inference in high level digital image analysis, we introduce a general extrinsic approach for data analysis on Hilbert manifolds with a focus on means of probability distributions on such sample…

This work proposes a novel channel estimator based on diffusion models (DMs), one of the currently top-rated generative models. Contrary to related works utilizing generative priors, a lightweight convolutional neural network (CNN) with…

In Bayesian inference for mixture models with an unknown number of components, a finite mixture model is usually employed that assumes prior distributions for mixing weights and the number of components. This model is called a mixture of…

This paper introduces a novel deep-learning-based approach for numerical simulation of a time-evolving Schr\"odinger equation inspired by stochastic mechanics and generative diffusion models. Unlike existing approaches, which exhibit…

A weighted likelihood technique for robust estimation of a multivariate Wrapped Normal distribution for data points scattered on a p-dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise…

This study presents a generative optimization framework that builds on a fine-tuned diffusion model and reward-directed sampling to generate high-performance engineering designs. The framework adopts a parametric representation of the…

Riemannian manifolds provide a principled way to model nonlinear geometric structure inherent in data. A Riemannian metric on said manifolds determines geometry-aware shortest paths and provides the means to define statistical models…

Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks. Here, we consider their use in the context of multivariate subsurface modeling and probabilistic inversion. We first demonstrate…

The Gaussian curvature of a two-dimensional Riemannian manifold is uniquely determined by the choice of the metric. The formulas for computing the curvature in terms of components of the metric, in isothermal coordinates, involve the…

Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative…

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,…

There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface…

This paper introduces posterior mean matching (PMM), a new method for generative modeling that is grounded in Bayesian inference. PMM uses conjugate pairs of distributions to model complex data of various modalities like images and text,…

In data-driven learning and inference tasks, the high cost of acquiring samples from the target distribution often limits performance. A common strategy to mitigate this challenge is to augment the limited target samples with data from a…

In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently…

With a view to statistical inference for discretely observed diffusion models, we propose simple methods of simulating diffusion bridges, approximately and exactly. Diffusion bridge simulation plays a fundamental role in likelihood and…

Knowledge of the noise distribution in diffusion MRI is the centerpiece to quantify uncertainties arising from the acquisition process. Accurate estimation beyond textbook distributions often requires information about the acquisition…

Motivated by population studies of Diffusion Tensor Imaging, the paper investigates the use of mean-based and dispersion-based permutation tests to define and compute the significance of a statistical test for data taking values on…

We propose a novel test for assessing partial effects in Frechet regression on Bures Wasserstein manifolds. Our approach employs a sample splitting strategy: the first subsample is used to fit the Frechet regression model, yielding…