Related papers: Flow matching on homogeneous spaces

Real-world data is often assumed to lie within a low-dimensional structure embedded in high-dimensional space. In practical settings, we observe only a finite set of samples, forming what we refer to as the sample data subspace. It serves…

In this contribution, a mathematical framework is constructed to relate and compare non-linear partial differential equations (PDEs) in the category of smooth manifolds. In particular, it can be used to compare those aspects of field…

We present two novel generative geometric deep learning frameworks, termed Flow Matching PointNet and Diffusion PointNet, for predicting fluid flow variables on irregular geometries by incorporating PointNet into flow matching and diffusion…

We begin a systematic study of these spaces, initially following along the lines of Eberlein's comprehensive study of the Riemannian case. In particular, we integrate the geodesic equation, discuss the structure of the isometry group, and…

Effective Hamiltonians arise in several problems, including homogenization of Hamilton--Jacobi equations, nonlinear control systems, Hamiltonian dynamics, and Aubry--Mather theory. In Aubry--Mather theory, related objects, Mather measures,…

We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free (SFdf) approximation based on a discrete $L^2$ projection. Within…

We present a new class of stochastic, geometrically-driven optimization algorithms on the orthogonal group $O(d)$ and naturally reductive homogeneous manifolds obtained from the action of the rotation group $SO(d)$. We theoretically and…

The Lie point symmetries and corresponding invariant solutions are obtained for a Gaussian, irrotational, compressible fluid flow. A supersymmetric extension of this model is then formulated through the use of a superspace and superfield…

Generative models based on flow matching have attracted significant attention for their simplicity and superior performance in high-resolution image synthesis. By leveraging the instantaneous change-of-variables formula, one can directly…

We consider the problem of density estimation on Riemannian manifolds. Density estimation on manifolds has many applications in fluid-mechanics, optics and plasma physics and it appears often when dealing with angular variables (such as…

Flow matching has recently emerged as a flexible and efficient framework for generative modelling by learning deterministic transport dynamics between probability measures. In this work, we extend flow matching to the space of probability…

Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these…

Sampling equilibrium distributions is fundamental to statistical mechanics. While flow matching has emerged as scalable state-of-the-art paradigm for generative modeling, its potential for equilibrium sampling in condensed-phase systems…

Foundational language models show a remarkable ability to learn new concepts during inference via context data. However, similar work for images lag behind. To address this challenge, we introduce FLoWN, a flow matching model that learns to…

We study Bayesian inverse problems with mixed noise, modeled as a combination of additive and multiplicative Gaussian components. While traditional inference methods often assume fixed or known noise characteristics, real-world…

We tackle the problem of estimating flow between two images with large lighting variations. Recent learning-based flow estimation frameworks have shown remarkable performance on image pairs with small displacement and constant…

The task of image restration is to find the spatial correspondence of two or more given images. In this paper we assume that the correspondence is given either by an Euclidean, or by an affine volume-preserving transformation. Since the…

Among plenty of applications, low-dimensional homogeneous spaces appear in cosmological models as both, classical factor spaces of multidimensional geometry and minisuperspaces in canonical quantization. Here a new tool to restrict their…

The acceleration of gradient-based optimization methods is a subject of significant practical and theoretical importance, particularly within machine learning applications. While much attention has been directed towards optimizing within…

We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups. We give the proof of the non-commutative integrability of flows and show, in addition, for…