Related papers: Manifold Generalization Provably Proceeds Memoriza…
We establish minimax convergence rates for score-based generative models (SGMs) under the $1$-Wasserstein distance. Assuming the target density $p^\star$ lies in a nonparametric $\beta$-smooth H\"older class with either compact support or…
Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…
Diffusion models now generate high-quality, diverse samples, with an increasing focus on more powerful models. Although ensembling is a well-known way to improve supervised models, its application to unconditional score-based diffusion…
Diffusion-based generative models demonstrate state-of-the-art performance across various image synthesis tasks, yet their tendency to replicate and amplify dataset biases remains poorly understood. Although previous research has viewed…
Diffusion probabilistic models have achieved remarkable success in generative tasks across diverse data types. While recent studies have explored alternative degradation processes beyond Gaussian noise, this paper bridges two key diffusion…
We investigate density estimation from a $n$-sample in the Euclidean space $\mathbb R^D$, when the data is supported by an unknown submanifold $M$ of possibly unknown dimension $d < D$ under a reach condition. We study nonparametric kernel…
Normalizing flows model a complex target distribution in terms of a bijective transform operating on a simple base distribution. As such, they enable tractable computation of a number of important statistical quantities, particularly…
Diffusion models have demonstrated remarkable performance in generating high-dimensional samples across domains such as vision, language, and the sciences. Although continuous-state diffusion models have been extensively studied both…
A $k$-modal probability distribution over the discrete domain $\{1,...,n\}$ is one whose histogram has at most $k$ "peaks" and "valleys." Such distributions are natural generalizations of monotone ($k=0$) and unimodal ($k=1$) probability…
Many measurements in computer vision and machine learning manifest as non-Euclidean data samples. Several researchers recently extended a number of deep neural network architectures for manifold valued data samples. Researchers have…
Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality.…
Recent advances in semi-supervised learning methods rely on estimating the categories of unlabeled data using a model trained on the labeled data (pseudo-labeling) and using the unlabeled data for various consistency-based regularization.…
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.…
Recently, diffusion model have demonstrated impressive image generation performances, and have been extensively studied in various computer vision tasks. Unfortunately, training and evaluating diffusion models consume a lot of time and…
Denoising Probabilistic Models (DPMs) represent an emerging domain of generative models that excel in generating diverse and high-quality images. However, most current training methods for DPMs often neglect the correlation between…
When do diffusion models reproduce their training data, and when are they able to generate samples beyond it? A practically relevant theoretical understanding of this interplay between memorization and generalization may significantly…
Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the…
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…
We consider a class of conditional forward-backward diffusion models for conditional generative modeling, that is, generating new data given a covariate (or control variable). To formally study the theoretical properties of these…
Deep Generative Models are frequently used to learn continuous representations of complex data distributions using a finite number of samples. For any generative model, including pre-trained foundation models with Diffusion or Transformer…