Related papers: Manifold Generalization Provably Proceeds Memoriza…
Practical diffusion sampling is a numerical approximation problem: under a fixed inference budget, one must simulate a reverse-time ODE or SDE using only a limited number of denoising steps, so discretization error is often the dominant…
Diffusion probabilistic models have become a cornerstone of modern generative AI, yet the mechanisms underlying their generalization remain poorly understood. In fact, if these models were perfectly minimizing their training loss, they…
Diffusion models generate samples by estimating the score function of the target distribution at various noise levels. The model is trained using samples drawn from the target distribution by progressively adding noise. Previous sample…
Diffusion Models (DMs), also referred to as score-based diffusion models, utilize neural networks to specify score functions. Unlike most other probabilistic models, DMs directly model the score functions, which makes them more flexible to…
We study the asymptotic error of score-based diffusion model sampling in large-sample scenarios from a non-parametric statistics perspective. We show that a kernel-based score estimator achieves an optimal mean square error of…
Diffusion models excel at generating high-quality, diverse samples, yet they risk memorizing training data when overfit to the training objective. We analyze the distinctions between memorization and generalization in diffusion models…
Diffusion models, though originally designed for generative tasks, have demonstrated impressive self-supervised representation learning capabilities. A particularly intriguing phenomenon in these models is the emergence of unimodal…
Diffusion models are capable of generating photo-realistic images that combine elements which likely do not appear together in the training set, demonstrating the ability to \textit{compositionally generalize}. Nonetheless, the precise…
Score-based models generate samples by mapping noise to data (and vice versa) via a high-dimensional diffusion process. We question whether it is necessary to run this entire process at high dimensionality and incur all the inconveniences…
Score-based diffusion models are a powerful class of generative models, but their practical use often depends on training neural networks to approximate the score function. Training-free diffusion models provide an attractive alternative by…
Diffusion models (DMs) are a powerful generative framework that have attracted significant attention in recent years. However, the high computational cost of training DMs limits their practical applications. In this paper, we start with a…
Conditional diffusion probabilistic models can model the distribution of natural images and can generate diverse and realistic samples based on given conditions. However, oftentimes their results can be unrealistic with observable color…
Estimating means on Riemannian manifolds is generally computationally expensive because the Riemannian distance function is not known in closed-form for most manifolds. To overcome this, we show that Riemannian diffusion means can be…
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…
Generalization in generative modeling is defined as the ability to learn an underlying distribution from a finite dataset and produce novel samples, with evaluation largely driven by held-out performance and perceived sample quality. In…
Manifold regularization is a commonly used technique in semi-supervised learning. It enforces the classification rule to be smooth with respect to the data-manifold. Here, we derive sample complexity bounds based on pseudo-dimension for…
Diffusion models have emerged as one of the most promising frameworks for deep generative modeling. In this work, we explore the potential of non-uniform diffusion models. We show that non-uniform diffusion leads to multi-scale diffusion…
The denoising diffusion model has recently emerged as a powerful generative technique, capable of transforming noise into meaningful data. While theoretical convergence guarantees for diffusion models are well established when the target…
A curious phenomenon observed in some dynamical generative models is the following: despite learning errors in the score function or the drift vector field, the generated samples appear to shift \emph{along} the support of the data…
Diffusion policies have shown impressive results in robot imitation learning, even for tasks that require satisfaction of kinematic equality constraints. However, task performance alone is not a reliable indicator of the policy's ability to…