Related papers: Generative Learning of Densities on Manifolds
Likelihood-based, or explicit, deep generative models use neural networks to construct flexible high-dimensional densities. This formulation directly contradicts the manifold hypothesis, which states that observed data lies on a…
The commonly used latent space embedding techniques, such as Principal Component Analysis, Factor Analysis, and manifold learning techniques, are typically used for learning effective representations of homogeneous data. However, they do…
Diffusion models have become a leading framework in generative modeling, yet their theoretical understanding -- especially for high-dimensional data concentrated on low-dimensional structures -- remains incomplete. This paper investigates…
Seismic imaging from sparsely acquired data faces challenges such as low image quality, discontinuities, and migration swing artifacts. Existing convolutional neural network (CNN)-based methods struggle with complex feature distributions…
Generative models have demonstrated strong performance in conditional settings and can be viewed as a form of data compression, where the condition serves as a compact representation. However, their limited controllability and…
As deep learning models grow in complexity and the volume of training data increases, reducing storage and computational costs becomes increasingly important. Dataset distillation addresses this challenge by synthesizing a compact set of…
Diffusion models recently developed for generative AI tasks can produce high-quality samples while still maintaining diversity among samples to promote mode coverage, providing a promising path for learning stochastic closure models.…
We present a supervised learning framework of training generative models for density estimation. Generative models, including generative adversarial networks, normalizing flows, variational auto-encoders, are usually considered as…
In this manuscript, we consider the problem of learning a flow or diffusion-based generative model parametrized by a two-layer auto-encoder, trained with online stochastic gradient descent, on a high-dimensional target density with an…
We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial Differential Equations (PDEs) discretized with structured…
There has been a growing interest in statistical inference from data satisfying the so-called manifold hypothesis, assuming data points in the high-dimensional ambient space to lie in close vicinity of a submanifold of much lower dimension.…
Generative models have enjoyed widespread success in a variety of applications. However, they encounter inherent mathematical limitations in modeling distributions where samples are constrained by equalities, as is frequently the setting in…
Deep generative models learn the data distribution, which is concentrated on a low-dimensional manifold. The geometric analysis of distribution transformation provides a better understanding of data structure and enables a variety of…
Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it.…
Diffusion models have recently driven significant breakthroughs in generative modeling. While state-of-the-art models produce high-quality samples on average, individual samples can still be low quality. Detecting such samples without human…
Building on the remarkable achievements in generative sampling of natural images, we propose an innovative challenge, potentially overly ambitious, which involves generating samples of entire multivariate time series that resemble images.…
This paper begins with a description of methods for estimating image probability density functions that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space-not…
Natural data observed in $\mathbb{R}^n$ is often constrained to an $m$-dimensional manifold $\mathcal{M}$, where $m < n$. This work focuses on the task of building theoretically principled generative models for such data. Current generative…
Graph diffusion models have made significant progress in learning structured graph data and have demonstrated strong potential for predictive tasks. Existing approaches typically embed node, edge, and graph-level features into a unified…
Obtaining accurate estimates of uncertainty in climate scenarios often requires generating large ensembles of high-resolution climate simulations, a computationally expensive and memory intensive process. To address this challenge, we train…