Related papers: Riemannian MeanFlow for One-Step Generation on Man…

Mainstream flow matching methods typically focus on learning the local velocity field, which inherently requires multiple integration steps during generation. In contrast, Mean Velocity Flow models establish a relationship between the local…

We introduce Random Projection Flows (RPFs), a principled framework for injective normalizing flows that leverages tools from random matrix theory and the geometry of random projections. RPFs employ random semi-orthogonal matrices, drawn…

Multistep inference is a bottleneck for real-time generative speech enhancement because flow- and diffusion-based systems learn an instantaneous velocity field and therefore rely on iterative ordinary differential equation (ODE) solvers. We…

We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the…

Reconstructing dynamical evolution from limited observations is a fundamental challenge in single-cell biology, where dynamic unbalanced optimal transport provides a principled framework for modeling coupled transport and mass variation.…

Graph-structured data jointly contain discrete topology and continuous geometry, which poses fundamental challenges for generative modeling due to heterogeneous distributions, incompatible noise dynamics, and the need for equivariant…

Flow-based image generative models exhibit stable training and produce high quality samples when using multi-step sampling procedures. One-step generative models can produce high quality image samples but can be difficult to optimize as…

Generative models like Flow Matching have achieved state-of-the-art performance but are often hindered by a computationally expensive iterative sampling process. To address this, recent work has focused on few-step or one-step generation by…

Robot manipulation has increasingly adopted data-driven generative policy frameworks, yet the field faces a persistent trade-off: diffusion models suffer from high inference latency, while flow-based methods often require complex…

Recently, studies on machine learning have focused on methods that use symmetry implicit in a specific manifold as an inductive bias. Grassmann manifolds provide the ability to handle fundamental shapes represented as shape spaces, enabling…

Generating high-quality time-series data is challenging because real-world signals often exhibit multimodal patterns and multiscale dynamics, including oscillations and high-frequency variations. Flow Matching (FM) offers an efficient…

Flow matching has recently emerged as a promising alternative to diffusion-based generative models, offering faster sampling and simpler training by learning continuous flows governed by ordinary differential equations. Despite growing…

Flow Matching has emerged as a powerful framework for learning continuous transformations between distributions, enabling high-fidelity generative modeling. This work introduces Symmetrical Flow Matching (SymmFlow), a new formulation that…

In this paper, we propose RiemannianFlow, a deep generative model that allows robots to learn complex and stable skills evolving on Riemannian manifolds. Examples of Riemannian data in robotics include stiffness (symmetric and positive…

MeanFlow enables one-step generation in continuous spaces by learning an average velocity over a time interval rather than the instantaneous velocity field of flow matching. However, discrete state spaces do not have smooth trajectories or…

We propose a unified, few-step generative modeling framework based on \emph{cumulative flow maps} for long-range transport in probability space, inspired by flow-map techniques for physical transport and dynamics. At its core is a…

Flow Matching has limited ability in achieving one-step generation due to its reliance on learned curved trajectories. Previous studies have attempted to address this limitation by either modifying the coupling distribution to prevent…

We present a comprehensive comparative study of three generative modeling paradigms: Denoising Diffusion Probabilistic Models (DDPM), Conditional Flow Matching (CFM), and MeanFlow. While DDPM and CFM require iterative sampling, MeanFlow…

Limited by inference latency, existing robot manipulation policies lack sufficient real-time interaction capability with the environment. Although faster generation methods such as flow matching are gradually replacing diffusion methods,…

Consistency models are a class of generative models that enable few-step generation for diffusion and flow matching models. While consistency models have achieved promising results on Euclidean domains like images, their applications to…