Related papers: Smoothing the Score Function for Generalization in…

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 have achieved remarkable success in generative modeling. However, this study confirms the existence of overfitting in diffusion model training, particularly in data-limited regimes. To address this challenge, we propose…

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…

Diffusion models are popular tools for generating new data samples, using a forward process that adds noise to data and a reverse process to denoise and produce samples. However, when the data distribution consists of n points, empirical…

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…

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…

Sampling from an unknown distribution, accessible only through discrete samples, is a fundamental problem at the core of generative AI. The current state-of-the-art methods follow a two-step process: first, estimating the score function…

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…

We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…

In this paper, we introduce a geometric framework to analyze memorization in diffusion models through the sharpness of the log probability density. We mathematically justify a previously proposed score-difference-based memorization metric…

Score matching is an approach to learning probability distributions parametrized up to a constant of proportionality (e.g. Energy-Based Models). The idea is to fit the score of the distribution, rather than the likelihood, thus avoiding the…

Generalization error predictors (GEPs) aim to predict model performance on unseen distributions by deriving dataset-level error estimates from sample-level scores. However, GEPs often utilize disparate mechanisms (e.g., regressors,…

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…

Imperfect score-matching leads to a shift between the training and the sampling distribution of diffusion models. Due to the recursive nature of the generation process, errors in previous steps yield sampling iterates that drift away from…

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…

Score-based diffusion modeling is a generative machine learning algorithm that can be used to sample from complex distributions. They achieve this by learning a score function, i.e., the gradient of the log-probability density of the data,…

Video summarization is a task of shortening a video by choosing a subset of frames while preserving its essential moments. Despite the innate subjectivity of the task, previous works have deterministically regressed to an averaged frame…

Real-world datasets are inherently heterogeneous, yet how per-class structural differences and sampling imbalance shape the training dynamics of diffusion models-and potentially exacerbate disparities-remains poorly understood. While models…

Diffusion models have recently emerged as a powerful framework for generative modeling. They consist of a forward process that perturbs input data with Gaussian white noise and a reverse process that learns a score function to generate…

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…