Related papers: A PDE Perspective on Generative Diffusion Models

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…

Diffusion models have been widely studied as effective generative tools for solving inverse problems. The main ideas focus on performing the reverse sampling process conditioned on noisy measurements, using well-established numerical…

Score-based stochastic denoising models have recently been demonstrated as powerful machine learning tools for conditional and unconditional image generation. The existing methods are based on a forward stochastic process wherein the…

Diffusion models have achieved great success in generating high-dimensional samples across various applications. While the theoretical guarantees for continuous-state diffusion models have been extensively studied, the convergence analysis…

There is a growing literature adopting a stochastic optimal control (SOC) perspective to fine-tune diffusion models and related generative policies. A prominent class of methods, known as iterative diffusion optimization, solves the SOC…

Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…

Turbulent flows posses broadband, power-law spectra in which multiscale interactions couple high-wavenumber fluctuations to large-scale dynamics. Although diffusion-based generative models offer a principled probabilistic forecasting…

Denoising diffusion models (DDMs) have recently attracted increasing attention by showing impressive synthesis quality. DDMs are built on a diffusion process that pushes data to the noise distribution and the models learn to denoise. In…

Beyond estimating parameters of interest from data, one of the key goals of statistical inference is to properly quantify uncertainty in these estimates. In Bayesian inference, this uncertainty is provided by the posterior distribution, the…

Statistical inference on large-dimensional tensor data has been extensively studied in the literature and widely used in economics, biology, machine learning, and other fields, but how to generate a structured tensor with a target…

Score-based generative models (SGMs) have recently emerged as a promising class of generative models. However, a fundamental limitation is that their inference is very slow due to a need for many (e.g., 2000) iterations of sequential…

For a considerable time, researchers have focused on developing a method that establishes a deep connection between the generative diffusion model and mathematical physics. Despite previous efforts, progress has been limited to the pursuit…

The score function for the diffusion process, also known as the gradient of the log-density, is a basic concept to characterize the probability flow with important applications in the score-based diffusion generative modelling and the…

Diffusion- and flow-based generative models have recently demonstrated strong performance in protein backbone generation tasks, offering unprecedented capabilities for de novo protein design. However, while achieving notable performance in…

Diffusion models have become a leading paradigm in generative AI, with score estimation via denoising score matching as a central component. While recent theory provides strong statistical guarantees, it typically relies on…

Consistency Models (CM) (Song et al., 2023) accelerate score-based diffusion model sampling at the cost of sample quality but lack a natural way to trade-off quality for speed. To address this limitation, we propose Consistency Trajectory…

Sampling based on score diffusions has led to striking empirical results, and has attracted considerable attention from various research communities. It depends on availability of (approximate) Stein score functions for various levels of…

Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…

Score-based generative models (SGMs) have achieved remarkable empirical success, motivating their application to a broad range of data distributions. However, extending them to heavy-tailed targets remains a largely open problem. Although…

Score-based diffusion generative models have recently emerged as a powerful tool for modelling complex data distributions. These models aim at learning the score function, which defines a map from a known probability distribution to the…