Related papers: Flow Matching on General Geometries

We propose a principled and effective framework for one-step generative modeling. We introduce the notion of average velocity to characterize flow fields, in contrast to instantaneous velocity modeled by Flow Matching methods. A…

Diffusion models can learn rich representations during data generation, showing potential for Self-Supervised Learning (SSL), but they face a trade-off between generative quality and discriminative performance. Their iterative sampling also…

Machine-learning (ML) techniques provide a new and encouraging perspective for constructing turbulence models for Reynolds-averaged Navier--Stokes (RANS) simulations. In this study, an iterative ML-RANS computational framework is proposed…

Recent advances in cross-modal few-shot adaptation treat visual-semantic alignment as a continuous feature transport problem via Flow Matching (FM). However, we argue that Euclidean-based FM overlooks fundamental limitations of flat…

Iterative generative models such as Flow Matching and Diffusion models have demonstrated strong test-time scaling behavior, where additional inference computation can improve generation quality. In contrast, Drift Models offer efficient…

Learning permutations is fundamental to sorting, ranking, and matching, but existing differentiable methods based on entropy-regularized Sinkhorn produce a single softened solution and collapse under ambiguity. We present PermFlow, a…

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…

We are interested in learning generative models for complex geometries described via manifolds, such as spheres, tori, and other implicit surfaces. Current extensions of existing (Euclidean) generative models are restricted to specific…

Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate…

Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples. Recent works, such as Flow Matching, derived paths that are optimal for each…

Learning accurate scene reconstruction without pose priors in neural radiance fields is challenging due to inherent geometric ambiguity. Recent development either relies on correspondence priors for regularization or uses off-the-shelf flow…

MeanFlow (MF) has recently been established as a framework for one-step generative modeling. However, its ``fastforward'' nature introduces key challenges in both the training objective and the guidance mechanism. First, the original MF's…

Enhancing the efficiency of high-quality image generation using Diffusion Models (DMs) is a significant challenge due to the iterative nature of the process. Flow Matching (FM) is emerging as a powerful generative modeling paradigm based on…

Multi-domain graph pre-training integrates knowledge from diverse domains to enhance performance in the target domains, which is crucial for building graph foundation models. Despite initial success, existing solutions often fall short of…

To better conform to data geometry, recent deep generative modelling techniques adapt Euclidean constructions to non-Euclidean spaces. In this paper, we study normalizing flows on manifolds. Previous work has developed flow models for…

Learning-based optical flow estimation has been dominated with the pipeline of cost volume with convolutions for flow regression, which is inherently limited to local correlations and thus is hard to address the long-standing challenge of…

We are interested in the challenging problem of modelling densities on Riemannian manifolds with a known symmetry group using normalising flows. This has many potential applications in physical sciences such as molecular dynamics and…

Simulating the long-time evolution of Hamiltonian systems is limited by the small timesteps required for stable numerical integration. To overcome this constraint, we introduce a framework to learn Hamiltonian Flow Maps by predicting the…

Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different…

Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean…