Related papers: Diffusion Models and the Manifold Hypothesis: Log-…
Diffusion models achieve remarkable generation quality, yet face a fundamental challenge known as memorization, where generated samples can replicate training samples exactly. We develop a theoretical framework to explain this phenomenon by…
Diffusion models have achieved remarkable progress in various domains with an intriguing ability to produce new data that do not exist in the training set. In this work, we study the hypothesis that such creativity arises from the neural…
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…
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 study the theoretical behavior of denoising score matching--the learning task associated to diffusion models--when the data distribution is supported on a low-dimensional manifold and the score is parameterized using a random feature…
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…
In this work, we propose a novel framework for estimating the dimension of the data manifold using a trained diffusion model. A diffusion model approximates the score function i.e. the gradient of the log density of a noise-corrupted…
Score-based methods, such as diffusion models and Bayesian inverse problems, are often interpreted as learning the data distribution in the low-noise limit ($\sigma \to 0$). In this work, we propose an alternative perspective: their success…
Score-based diffusion models are a highly effective method for generating samples from a distribution of images. We consider scenarios where the training data comes from a noisy version of the target distribution, and present an efficiently…
The success of denoising diffusion models raises important questions regarding their generalisation behaviour, particularly in high-dimensional settings. Notably, it has been shown that when training and sampling are performed perfectly,…
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…
We study a data-dependent notion of diffusion-model generalization: when a model does not memorize the training set, where do its generated samples go relative to the geometry induced by the data? To answer this, we introduce a…
We study counterfactual distribution learning for high-dimensional outcomes whose counterfactual law may concentrate near lower-dimensional structure. Standard isotropic smoothing treats all ambient directions equally, leading to…
Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world…
How diffusion models generalize beyond their training set is not known, and is somewhat mysterious given two facts: the optimum of the denoising score matching (DSM) objective usually used to train diffusion models is the score function of…
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.…
Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
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,…
Discrete-time diffusion-based generative models and score matching methods have shown promising results in modeling high-dimensional image data. Recently, Song et al. (2021) show that diffusion processes that transform data into noise can…
Euclidean diffusion models have achieved remarkable success in generative modeling across diverse domains, and they have been extended to manifold cases in recent advances. Instead of explicitly utilizing the structure of special manifolds…