Related papers: Generative Modelling with High-Order Langevin Dyna…
Diffusion/score-based models have emerged as powerful generative models, capable of generating high-quality samples that mimic the training data distribution. However, it has been observed that they are prone to reproducing training…
Denoising diffusion probabilistic models (DDPMs) represent an entirely new class of generative AI methods that have yet to be fully explored. They use Langevin dynamics, represented as stochastic differential equations, to describe a…
We introduce a novel class of score-based diffusion processes that operate directly in the representation space of Lie groups. Leveraging the framework of Generalized Score Matching, we derive a class of Langevin dynamics that decomposes as…
We introduce a new generative model where samples are produced via Langevin dynamics using gradients of the data distribution estimated with score matching. Because gradients can be ill-defined and hard to estimate when the data resides on…
Score-based generative models (SGMs) have demonstrated remarkable synthesis quality. SGMs rely on a diffusion process that gradually perturbs the data towards a tractable distribution, while the generative model learns to denoise. The…
Multiscale dynamical systems characterized by interacting fast and slow processes are ubiquitous across scientific domains, from climate dynamics to fluid mechanics. Accurate modeling of such systems requires capturing both the long-term…
Score-based generative models have demonstrated significant practical success in data-generating tasks. The models establish a diffusion process that perturbs the ground truth data to Gaussian noise and then learn the reverse process to…
Score-based generative models based on stochastic differential equations (SDEs) achieve impressive performance in sampling from unknown distributions, but often fail to satisfy underlying constraints. We propose a constrained generative…
Score-based Generative Models (SGMs) have demonstrated exceptional synthesis outcomes across various tasks. However, the current design landscape of the forward diffusion process remains largely untapped and often relies on physical…
Score-based generative models (SGMs) have recently demonstrated impressive results in terms of both sample quality and distribution coverage. However, they are usually applied directly in data space and often require thousands of network…
Score-based generative models (SGMs) have recently emerged as a promising class of generative models. However, a fundamental limitation is that their sampling process is slow due to a need for many (e.g., 2000) iterations of sequential…
Generating graph-structured data requires learning the underlying distribution of graphs. Yet, this is a challenging problem, and the previous graph generative methods either fail to capture the permutation-invariance property of graphs or…
We introduce a constructive framework to learn effective Langevin equations from stationary time series. Unlike conventional approaches that require iterative calibration to match target statistics, our construction guarantees the observed…
Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting…
Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audios, and point clouds. Recently, the deep connection between forward-backward stochastic differential equations…
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…
This report presents the comprehensive implementation, evaluation, and optimization of Denoising Diffusion Probabilistic Models (DDPMs) and Denoising Diffusion Implicit Models (DDIMs), which are state-of-the-art generative models. During…
Score-based generative modeling (SBGM) has achieved state-of-the-art performance in image generation, with the quality of generated images being highly dependent on the design of the forward (diffusion) process. Among these, models based on…
Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…
Langevin dynamics sampling suffers from extremely low generation speed, fundamentally limited by numerous fine-grained iterations to converge to the target distribution. We introduce PID-controlled Langevin Dynamics (PIDLD), a novel…