Related papers: Diffusion Geometry
A central problem in data analysis is the low dimensional representation of high dimensional data, and the concise description of its underlying geometry and density. In the analysis of large scale simulations of complex dynamical systems,…
Diffusion models have been central to the development of recent image, video, and even text generation systems. They posses striking geometric properties that can be faithfully portrayed in low-dimensional settings. However, existing…
Computing sample means on Riemannian manifolds is typically computationally costly as exemplified by computation of the Fr\'echet mean which often requires finding minimizing geodesics to each data point for each step of an iterative…
Inspired by random walk on graphs, diffusion map (DM) is a class of unsupervised machine learning that offers automatic identification of low-dimensional data structure hidden in a high-dimensional dataset. In recent years, among its many…
Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standard approach is first to discretize and then to apply…
We present Manifold Diffusion Fields (MDF), an approach that unlocks learning of diffusion models of data in general non-Euclidean geometries. Leveraging insights from spectral geometry analysis, we define an intrinsic coordinate system on…
The surrounding world surprises us by the beauty and variety of complex shapes that emerge from nanometric to macroscopic scales. Natural or manufactured materials (sandstones, sedimentary rocks and cement), colloidal solutions (proteins…
Molecular dynamics (MD) has long been the de facto choice for simulating complex atomistic systems from first principles. Recently deep learning models become a popular way to accelerate MD. Notwithstanding, existing models depend on…
Homology-based invariants can be used to characterize the geometry of datasets and thereby gain some understanding of the processes generating those datasets. In this work we investigate how the geometry of a dataset changes when it is…
Diffusion models, as a novel generative paradigm, have achieved remarkable success in various image generation tasks such as image inpainting, image-to-text translation, and video generation. Graph generation is a crucial computational task…
Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and…
Score-based generative models exhibit state of the art performance on density estimation and generative modeling tasks. These models typically assume that the data geometry is flat, yet recent extensions have been developed to synthesize…
Mapper, a topological algorithm, is frequently used as an exploratory tool to build a graphical representation of data. This representation can help to gain a better understanding of the intrinsic shape of high-dimensional genomic data and…
Choosing the Fisher information as the metric tensor for a Riemannian manifold provides a powerful yet fundamental way to understand statistical distribution families. Distances along this manifold become a compelling measure of statistical…
Diffusion Probabilistic Methods are employed for state-of-the-art image generation. In this work, we present a method for extending such models for performing image segmentation. The method learns end-to-end, without relying on a…
Diffusion models excel in content generation by implicitly learning the data manifold, yet they lack a practical method to leverage this manifold - unlike other deep generative models equipped with latent spaces. This paper introduces a…
Diffusion models (DMs) have emerged as powerful tools for modeling complex data distributions and generating realistic new samples. Over the years, advanced architectures and sampling methods have been developed to make these models…
An unsupervised learning algorithm to cluster hyperspectral image (HSI) data is proposed that exploits spatially-regularized random walks. Markov diffusions are defined on the space of HSI spectra with transitions constrained to near…
An increasingly common viewpoint is that protein dynamics data sets reside in a non-linear subspace of low conformational energy. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The…
Big data often has emergent structure that exists at multiple levels of abstraction, which are useful for characterizing complex interactions and dynamics of the observations. Here, we consider multiple levels of abstraction via a…