Related papers: Total Variation Rates for Riemannian Flow Matching

Generating high-dimensional visual modalities is a computationally intensive task. A common solution is progressive generation, where the outputs are synthesized in a coarse-to-fine spectral autoregressive manner. While diffusion models…

Flow matching (FM) constructs continuous-time ODE samplers by prescribing probability paths between a base distribution and a target distribution. In this note, we study FM through the lens of finite-sample plug-in estimation. In addition…

We introduce an unsupervised approach for constructing a global reference system by learning, in the ambient space, vector fields that span the tangent spaces of an unknown data manifold. In contrast to isometric objectives, which…

We propose a variational form of the BDF2 method as an alternative to the commonly used minimizing movement scheme for the time-discrete approximation of gradient flows in abstract metric spaces. Assuming uniform semi-convexity --- but no…

In this paper, we are interested in the application to video segmentation of the discrete shape optimization problem involving the shape weighted perimeter and an additional term depending on a parameter. Based on recent works and in…

This paper proposes a novel method, Explicit Flow Matching (ExFM), for training and analyzing flow-based generative models. ExFM leverages a theoretically grounded loss function, ExFM loss (a tractable form of Flow Matching (FM) loss), to…

Recent efforts have extended the flow-matching framework to discrete generative modeling. One strand of models directly works with the continuous probabilities instead of discrete tokens, which we colloquially refer to as Continuous-State…

We analyze inexact Riemannian gradient descent (RGD) where Riemannian gradients and retractions are inexactly (and cheaply) computed. Our focus is on understanding when inexact RGD converges and what is the complexity in the general…

We consider the statistical analysis of trajectories on Riemannian manifolds that are observed under arbitrary temporal evolutions. Past methods rely on cross-sectional analysis, with the given temporal registration, and consequently may…

In this paper, we propose the Graph-Fused Multivariate Regression (GFMR) via Total Variation regularization, a novel method for estimating the association between a one-dimensional or multidimensional array outcome and scalar predictors.…

The Teichm\"uller harmonic map flow is a gradient flow for the harmonic map energy of maps from a closed surface to a general closed Riemannian target manifold of any dimension, where both the map and the domain metric are allowed to…

We investigate some previously unexplored (or underexplored) computational aspects of total variation (TV) distance. First, we give a simple deterministic polynomial-time algorithm for checking equivalence between mixtures of product…

This work considers the use of Total variation (TV) minimization in the recovery of a given gradient sparse vector from Gaussian linear measurements. It has been shown in recent studies that there exist a sharp phase transition behavior in…

Diffusion model (DM)-based channel estimation, which generates channel samples via a posteriori sampling stepwise with denoising process, has shown potential in high-precision channel state information (CSI) acquisition. However, slow…

Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…

Dense image correspondence is central to many applications, such as visual odometry, 3D reconstruction, object association, and re-identification. Historically, dense correspondence has been tackled separately for wide-baseline scenarios…

Forecasting conditional stochastic nonlinear dynamical systems is a fundamental challenge repeatedly encountered across the biological and physical sciences. While flow-based models can impressively predict the temporal evolution of…

Despite the widespread success of Transformers across various domains, their optimization guarantees in large-scale model settings are not well-understood. This paper rigorously analyzes the convergence properties of gradient flow in…

We obtain height, gradient, and curvature a priori estimates for a modified mean curvature flow in Riemannian manifolds endowed with a Killing vector field. As a consequence, we prove the existence of smooth, entire, longtime solutions for…

We propose \emph{Euler Mean Flows (EMF)}, a flow-based generative framework for one-step and few-step generation that enforces long-range trajectory consistency with minimal sampling cost. The key idea of EMF is to replace the trajectory…