相关论文: Riemannian Score-Based Generative Modelling

Physics-inspired Generative Models (GMs), in particular Diffusion Models (DMs) and Poisson Flow Models (PFMs), enhance Bayesian methods and promise great utility in medical imaging. This review examines the transformative role of such…

This paper studies stable learning methods for generative models that enable high-quality data generation. Noise injection is commonly used to stabilize learning. However, selecting a suitable noise distribution is challenging.…

Guiding Vector Fields (GVFs) are a powerful tool for robotic path following. However, classical methods assume smooth, ordered curves and fail when paths are unordered, multi-branch, or generated by probabilistic models. We propose a…

Recent developments in generative modeling have utilized score-based methods coupled with stochastic differential equations to sample from complex probability distributions. However, these and other performant sampling methods generally…

Idempotent generative networks (IGNs) are a new line of generative models based on idempotent mapping to a target manifold. IGNs support both single-and multi-step generation, allowing for a flexible trade-off between computational cost and…

In dynamical systems characterized by separation of time scales, the approximation of so called ``slow manifolds'', on which the long term dynamics lie, is a useful step for model reduction. Initializing on such slow manifolds is a useful…

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…

This paper explores the use of score-based diffusion models for Bayesian image reconstruction. Diffusion models are an efficient tool for generative modeling. Diffusion models can also be used for solving image reconstruction problems. We…

Recent work has explored a range of model families for human motion generation, including Variational Autoencoders (VAEs), Generative Adversarial Networks (GANs), and diffusion-based models. Despite their differences, many methods rely on…

Contemporary work implies generative machine learning models are capable of learning the phase behavior in condensed matter systems such as the Ising model. In this Letter, we utilize a score-based modeling procedure called Thermodynamic…

Most existing generative models are limited to learning a single probability distribution from the training data and cannot generalize to novel distributions for unseen data. An architecture that can generate samples from both trained…

Generative diffusion processes are an emerging and effective tool for image and speech generation. In the existing methods, the underline noise distribution of the diffusion process is Gaussian noise. However, fitting distributions with…

Data-driven Riemannian geometry has emerged as a powerful tool for interpretable representation learning, offering improved efficiency in downstream tasks. Moving forward, it is crucial to balance cheap manifold mappings with efficient…

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 diffusion models have emerged as a powerful class of generative methods, achieving state-of-the-art performance across diverse domains. Despite their empirical success, the mathematical foundations of those models remain only…

Diffusion models have emerged as powerful deep generative techniques, producing high-quality and diverse samples in applications in various domains including audio. While existing reviews provide overviews, there remains limited in-depth…

Probabilistic graphical models (PGMs) are powerful tools for representing statistical dependencies through graphs in high-dimensional systems. However, they are limited to pairwise interactions. In this work, we propose the simplicial…

Generative diffusion models synthesize new samples by reversing a diffusive process that converts a given data set to generic noise. This is accomplished by training a neural network to match the gradient of the log of the probability…

Seismic imaging from sparsely acquired data faces challenges such as low image quality, discontinuities, and migration swing artifacts. Existing convolutional neural network (CNN)-based methods struggle with complex feature distributions…

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…