Related papers: (Deep) Generative Geodesics
The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a principal notion of geometry without restrictive assumptions on either the model or the data…
We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the…
Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data. These representations, however, tend to much distort relationships between points, i.e. pairwise distances…
Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate…
The length of the geodesic between two data points along a Riemannian manifold, induced by a deep generative model, yields a principled measure of similarity. Current approaches are limited to low-dimensional latent spaces, due to the…
Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the…
We propose a geometric latent-subspace framework for generative modeling of discrete data. Specifically, we introduce latent subspaces in the exponential parameter space of product manifolds of categorical distributions as a novel method…
Deep generative models are universal tools for learning data distributions on high dimensional data spaces via a mapping to lower dimensional latent spaces. We provide a study of latent space geometries and extend and build upon previous…
Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator…
We propose a manifold matching approach to generative models which includes a distribution generator (or data generator) and a metric generator. In our framework, we view the real data set as some manifold embedded in a high-dimensional…
Recent breakthroughs and rapid integration of generative models (GMs) have sparked interest in the problem of model attribution and their fingerprints. For instance, service providers need reliable methods of authenticating their models to…
Riemannian geometry provides us with powerful tools to explore the latent space of generative models while preserving the underlying structure of the data. The latent space can be equipped it with a Riemannian metric, pulled back from the…
Generative adversarial networks (GANs) have emerged as a powerful unsupervised method to model the statistical patterns of real-world data sets, such as natural images. These networks are trained to map random inputs in their latent space…
This paper introduces a new metric and mean on the set of positive semidefinite matrices of fixed-rank. The proposed metric is derived from a well-chosen Riemannian quotient geometry that generalizes the reductive geometry of the positive…
The theory of geodesic regression aims to find a geodesic curve which is an optimal fit to a given set of data. In this article we restrict ourselves to the Riemannian manifold of positive definite operators (matrices) on a Hilbert space of…
Stochastic generative models enable us to capture the geometric structure of a data manifold lying in a high dimensional space through a Riemannian metric in the latent space. However, its practical use is rather limited mainly due to…
Content and image generation consist in creating or generating data from noisy information by extracting specific features such as texture, edges, and other thin image structures. We are interested here in generative models, and two main…
Modern generative models can produce realistic samples, however, balancing memorisation and generalisation remains an open problem. We approach this challenge from a Bayesian perspective by focusing on the parameter space of flow matching…
Deep generative models like variational autoencoders approximate the intrinsic geometry of high dimensional data manifolds by learning low-dimensional latent-space variables and an embedding function. The geometric properties of these…
Riemannian metric learning is an emerging field in machine learning, unlocking new ways to encode complex data structures beyond traditional distance metric learning. While classical approaches rely on global distances in Euclidean space,…