Related papers: Asymptotic Learning Curves for Diffusion Models wi…

Many recent works utilize denoising score matching to optimize the conditional input of diffusion models. In this workshop paper, we demonstrate that such optimization breaks the equivalence between denoising score matching and exact score…

Denoising Score Matching estimates the score of a noised version of a target distribution by minimizing a regression loss and is widely used to train the popular class of Denoising Diffusion Models. A well known limitation of Denoising…

The predominant success of diffusion models in generative modeling has spurred significant interest in understanding their theoretical foundations. In this work, we propose a feature learning framework aimed at analyzing and comparing the…

We examine theoretical properties of the denoising score matching estimate. We model the density of observations with a nonparametric Gaussian mixture. We significantly relax the standard manifold assumption allowing the samples step away…

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…

Reversing a diffusion process by learning its score forms the heart of diffusion-based generative modeling and for estimating properties of scientific systems. The diffusion processes that are tractable center on linear processes with a…

Score-based models have achieved remarkable results in the generative modeling of many domains. By learning the gradient of smoothed data distribution, they can iteratively generate samples from complex distribution e.g. natural images.…

Recent work on diffusion models proposed that they operate in two regimes: memorization, in which models reproduce their training data, and generalization, in which they generate novel samples. While this has been tested in high-noise…

In this work, we study the generalizability of diffusion models by looking into the hidden properties of the learned score functions, which are essentially a series of deep denoisers trained on various noise levels. We observe that as…

Score-based diffusion models generate new samples by learning the score function associated with a diffusion process. While the effectiveness of these models can be theoretically explained using differential equations related to the…

Diffusion models have emerged as the principal paradigm for generative modeling across various domains. During training, they learn the score function, which in turn is used to generate samples at inference. They raise a basic yet unsolved…

Score diffusion methods can learn probability densities from samples. The score of the noise-corrupted density is estimated using a deep neural network, which is then used to iteratively transport a Gaussian white noise density to a target…

This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…

Score-based diffusion models provide a powerful way to model images using the gradient of the data distribution. Leveraging the learned score function as a prior, here we introduce a way to sample data from a conditional distribution given…

Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their…

Deep neural networks (DNNs) trained for image denoising are able to generate high-quality samples with score-based reverse diffusion algorithms. These impressive capabilities seem to imply an escape from the curse of dimensionality, but…

Diffusion models often generate novel samples even when the learned score is only \emph{coarse} -- a phenomenon not accounted for by the standard view of diffusion training as density estimation. In this paper, we show that, under the…

While the manifold hypothesis is widely adopted in modern machine learning, complex data is often better modeled as stratified spaces -- unions of manifolds (strata) of varying dimensions. Stratified learning is challenging due to varying…

As a class of generative artificial intelligence frameworks inspired by statistical physics, diffusion models have shown extraordinary performance in synthesizing complicated data distributions through a denoising process gradually guided…

Denoising diffusions are state-of-the-art generative models exhibiting remarkable empirical performance. They work by diffusing the data distribution into a Gaussian distribution and then learning to reverse this noising process to obtain…