Related papers: Total Variation Rates for Riemannian Flow Matching
Modeling distributions on Riemannian manifolds is a crucial component in understanding non-Euclidean data that arises, e.g., in physics and geology. The budding approaches in this space are limited by representational and computational…
This paper proposes a vision-conditioned flow matching (FM) framework for beam prediction in millimeter-wave vehicle-to-infrastructure links. Instead of modeling discrete beam-index sequences, the proposed method learns the temporal…
We define rigorously a solution to the fourth-order total variation flow equation in $\mathbb{R}^n$. If $n\geq3$, it can be understood as a gradient flow of the total variation energy in $D^{-1}$, the dual space of $D^1_0$, which is the…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
We study geometric properties of the gradient flow for learning deep linear convolutional networks. For linear fully connected networks, it has been shown recently that the corresponding gradient flow on parameter space can be written as a…
Many measurements in computer vision and machine learning manifest as non-Euclidean data samples. Several researchers recently extended a number of deep neural network architectures for manifold valued data samples. Researchers have…
Deep homography estimation has broad applications in computer vision and robotics. Remarkable progresses have been achieved while the existing methods typically treat it as a direct regression or iterative refinement problem and often…
Total variation (TV) minimization is one of the most important techniques in modern signal/image processing, and has wide range of applications. While there are numerous recent works on the restoration guarantee of the TV minimization in…
We introduce an ordinary differential equation (ODE) based deep generative method for learning conditional distributions, named Conditional F\"ollmer Flow. Starting from a standard Gaussian distribution, the proposed flow could approximate…
This paper introduces the sigma flow model for the prediction of structured labelings of data observed on Riemannian manifolds, including Euclidean image domains as special case. The approach combines the Laplace-Beltrami framework for…
We study the identification of continuous-time vector fields from irregularly sampled trajectories. We introduce spectral flow learning, which learns in a windowed flow space using a lag-linear label operator that aggregates lagged Koopman…
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…
Recent learning-based methods for event-based optical flow estimation utilize cost volumes for pixel matching but suffer from redundant computations and limited scalability to higher resolutions for flow refinement. In this work, we take…
Rectified Flow offers a simple and effective approach to high-quality generative modeling by learning a velocity field. However, we identify a limitation in directly modeling the velocity with an unconstrained neural network: the learned…
Optical flow is a fundamental technique for motion estimation, widely applied in video stabilization, interpolation, and object tracking. Traditional optical flow estimation methods rely on restrictive assumptions like brightness constancy…
Diffusion and flow matching models have significantly advanced media generation, yet their design space is well-explored, somewhat limiting further improvements. Concurrently, autoregressive (AR) models, particularly those generating…
Mean flow (MeanFlow) enables efficient, high-fidelity image generation, yet its single-function evaluation (1-NFE) generation often cannot yield compelling results. We address this issue by introducing RMFlow, an efficient multimodal…
This paper investigates the connections between rectified flows, flow matching, and optimal transport. Flow matching is a recent approach to learning generative models by estimating velocity fields that guide transformations from a source…
This work is about the total variation (TV) minimization which is used for recovering gradient-sparse signals from compressed measurements. Recent studies indicate that TV minimization exhibits a phase transition behavior from failure to…
A flow matching model learns a time-dependent vector field $v_t(x)$ that generates a probability path $\{ p_t \}_{0 \leq t \leq 1}$ that interpolates between a well-known noise distribution ($p_0$) and the data distribution ($p_1$). It can…