Related papers: Functional Mean Flow in Hilbert Space

We propose Manifold Free-Form Flows (M-FFF), a simple new generative model for data on manifolds. The existing approaches to learning a distribution on arbitrary manifolds are expensive at inference time, since sampling requires solving a…

Recent studies suggest utilizing generative models instead of traditional auto-regressive algorithms for time series forecasting (TSF) tasks. These non-auto-regressive approaches involving different generative methods, including GAN,…

Flow Matching is a powerful framework for learning transport maps between probability distributions. Yet its standard single-parameter formulation is not designed to capture multi-parameter variations where the resulting transport should be…

Continuous diffusion and flow matching models could represent a powerful alternative to autoregressive approaches for language modelling (LM), as they unlock a host of advantages currently reserved for continuous modalities, including…

Generative policies based on diffusion and flow matching achieve strong performance in robotic manipulation by modeling multi-modal human demonstrations. However, their reliance on iterative Ordinary Differential Equation (ODE) integration…

Optical flow is a powerful tool for the study and analysis of motion in a sequence of images. In this article we study a Horn-Schunck type spatio-temporal regularization functional for image sequences that have a non-Euclidean, time varying…

Accurate emulation of multi-scale physical systems governed by PDEs demands models that remain stable over long autoregressive rollouts while preserving fine-scale structures. Deterministic emulators produce overly-smoothed predictions,…

We propose a machine learning framework based on Flow Matching (FM) to identify critical properties in many-body systems efficiently. Using the 2D XY model as a benchmark, we demonstrate that a single network, trained only on configurations…

This paper introduces the concept of functional current as a mathematical framework to represent and treat functional shapes, i.e. sub-manifold supported signals. It is motivated by the growing occurrence, in medical imaging and…

Flow Matching (FM) has recently emerged as a leading approach for high-fidelity visual generation, offering a robust continuous-time alternative to ordinary differential equation (ODE) based models. However, despite their success, FM models…

Flow-based generative models have demonstrated promising performance across a broad spectrum of data modalities (e.g., image and text). However, there are few works exploring their extension to unordered data (e.g., spatial point set),…

MeanFlow promises high-quality generative modeling in few steps, by jointly learning instantaneous and average velocity fields. Yet, the underlying training dynamics remain unclear. We analyze the interaction between the two velocities and…

The multi-step denoising process in diffusion and Flow Matching models causes major efficiency issues, which motivates research on few-step generation. We present Solution Flow Models (SoFlow), a framework for one-step generation from…

Diffusion-based unsupervised image registration has been explored for cardiac cine MR, but expensive multi-step inference limits practical use. We propose FlowReg, a flow-matching framework in displacement field space that achieves strong…

The control flow graph (CFG) representation of a procedure used by virtually all flow-sensitive program analyses, admits a large number of infeasible control flow paths i.e., these paths do not occur in any execution of the program. Hence…

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…

Continuous normalizing flows (CNFs) learn an ordinary differential equation to transform prior samples into data. Flow matching (FM) has recently emerged as a simulation-free approach for training CNFs by regressing a velocity model towards…

Optical flow estimation is a fundamental problem in computer vision, yet the reliance on expensive ground-truth annotations limits the scalability of supervised approaches. Although unsupervised and semi-supervised methods alleviate this…

Flow maps enable high-quality image generation in a single forward pass. However, unlike iterative diffusion models, their lack of an explicit sampling trajectory impedes incorporating external constraints for conditional generation and…

Deep learning models have emerged as a powerful tool for various medical applications. However, their success depends on large, high-quality datasets that are challenging to obtain due to privacy concerns and costly annotation. Generative…