Related papers: Riemannian Neural Geodesic Interpolant

Progressively applying Gaussian noise transforms complex data distributions to approximately Gaussian. Reversing this dynamic defines a generative model. When the forward noising process is given by a Stochastic Differential Equation (SDE),…

Generating continuous environmental models from sparsely sampled data is a critical challenge in spatial modeling, particularly for topography. Traditional spatial interpolation methods often struggle with handling sparse measurements. To…

Motivated by the computational difficulties incurred by popular deep learning algorithms for the generative modeling of temporal densities, we propose a cheap alternative which requires minimal hyperparameter tuning and scales favorably to…

We describe, in an intrinsic way and using the global chart provided by Ito's parallel transport, a generalisation of the notion of geodesic (as critical path of an energy functional) to diffusion processes on Riemannian manifolds. These…

Flow Matching enables simulation-free training of generative models on Riemannian manifolds, yet sampling typically still relies on numerically integrating a probability-flow ODE. We propose Riemannian MeanFlow (RMF), extending MeanFlow to…

Stochastic interpolants offer a robust framework for continuously transforming samples between arbitrary data distributions, holding significant promise for generative modeling. Despite their potential, rigorous finite-time convergence…

Sequential models like recurrent neural networks and transformers have become standard for probabilistic multivariate time series forecasting across various domains. Despite their strengths, they struggle with capturing high-dimensional…

Neural samplers such as variational autoencoders (VAEs) or generative adversarial networks (GANs) approximate distributions by transforming samples from a simple random source---the latent space---to samples from a more complex distribution…

This paper focus on investigating the distributed Riemannian stochastic optimization problem on the Stiefel manifold for multi-agent systems, where all the agents work collaboratively to optimize a function modeled by the average of their…

Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a ``noising'' stage, whereby a diffusion is used to gradually…

We present Extended Riemannian Stochastic Derivative-Free Optimization (Extended RSDFO), a novel population-based stochastic optimization algorithm on Riemannian manifolds that addresses the locality and implicit assumptions of manifold…

We introduce an optimal transport-based model for learning a metric tensor from cross-sectional samples of evolving probability measures on a common Riemannian manifold. We neurally parametrize the metric as a spatially-varying matrix field…

Decentralized optimization on Riemannian manifolds is foundational for many modern machine learning and signal processing applications in which data are non-Euclidean and generated and processed in a distributed manner. Although intrinsic…

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…

In this work, we propose to study the global geometrical properties of generative models. We introduce a new Riemannian metric to assess the similarity between any two data points. Importantly, our metric is agnostic to the parametrization…

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…

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…

Diffusion bridge models and stochastic interpolants enable high-quality image-to-image (I2I) translation by creating paths between distributions in pixel space. However, the proliferation of techniques based on incompatible mathematical…

Transport-based methods have emerged as a leading paradigm for building generative models from large, clean datasets. However, in many scientific and engineering domains, clean data are often unavailable: instead, we only observe…

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…