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Continuous-time generative models, such as Flow Matching (FM), construct probability paths to transport between one distribution and another through the simulation-free learning of the neural ordinary differential equations (ODEs). During…

Machine Learning · Computer Science 2024-05-24 Qunxi Zhu , Wei Lin

We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate in infinite-dimensional spaces. Our approach works by first defining a path of probability…

Machine Learning · Computer Science 2023-12-07 Gavin Kerrigan , Giosue Migliorini , Padhraic Smyth

Normalizing flows model a complex target distribution in terms of a bijective transform operating on a simple base distribution. As such, they enable tractable computation of a number of important statistical quantities, particularly…

Machine Learning · Computer Science 2022-09-01 Chandramouli Shama Sastry , Andreas Lehrmann , Marcus Brubaker , Alexander Radovic

We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…

Machine Learning · Computer Science 2026-05-11 Aditya Ranganath , Mukesh Singhal

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…

Machine Learning · Computer Science 2025-11-17 Wenkai Liu , Nan Ma , Jianqiao Chen , Xiaoxuan Qi , Yuhang Ma

Rectified flow and reflow procedures have significantly advanced fast generation by progressively straightening ordinary differential equation (ODE) flows. They operate under the assumption that image and noise pairs, known as couplings,…

Machine Learning · Computer Science 2024-11-04 Dogyun Park , Sojin Lee , Sihyeon Kim , Taehoon Lee , Youngjoon Hong , Hyunwoo J. Kim

Flow Matching (FM) is a recent generative modelling technique: we aim to learn how to sample from distribution $\mathfrak{X}_1$ by flowing samples from some distribution $\mathfrak{X}_0$ that is easy to sample from. The key trick is that…

Differential Geometry · Mathematics 2025-10-24 Finn M. Sherry , Bart M. N. Smets

Inverse design aims to find design parameters $x$ achieving target performance $y^*$. Generative approaches learn bidirectional mappings between designs and labels, enabling diverse solution sampling. However, standard conditional flow…

Machine Learning · Computer Science 2026-03-18 Miguel de Campos , Werner Krebs , Hanno Gottschalk

Diffusion models have exhibited excellent performance in various domains. The probability flow ordinary differential equation (ODE) of diffusion models (i.e., diffusion ODEs) is a particular case of continuous normalizing flows (CNFs),…

Machine Learning · Computer Science 2024-04-09 Kaiwen Zheng , Cheng Lu , Jianfei Chen , Jun Zhu

Mean field control (MFC) problems have vast applications in artificial intelligence, engineering, and economics, while solving MFC problems accurately and efficiently in high-dimensional spaces remains challenging. This work introduces…

Optimization and Control · Mathematics 2025-03-26 Jiaxi Zhao , Mo Zhou , Xinzhe Zuo , Wuchen Li

Catastrophic forgetting (CF) happens whenever a neural network overwrites past knowledge while being trained on new tasks. Common techniques to handle CF include regularization of the weights (using, e.g., their importance on past tasks),…

Machine Learning · Statistics 2021-08-06 Jary Pomponi , Simone Scardapane , Aurelio Uncini

By chaining a sequence of differentiable invertible transformations, normalizing flows (NF) provide an expressive method of posterior approximation, exact density evaluation, and sampling. The trend in normalizing flow literature has been…

Machine Learning · Computer Science 2020-10-20 Robert Giaquinto , Arindam Banerjee

Flow-based generative models have highly desirable properties like exact log-likelihood evaluation and exact latent-variable inference, however they are still in their infancy and have not received as much attention as alternative…

Computer Vision and Pattern Recognition · Computer Science 2020-04-06 Albert Pumarola , Stefan Popov , Francesc Moreno-Noguer , Vittorio Ferrari

We explore a generative machine learning-based approach for estimating multi-dimensional probability density functions (PDFs) in a target sample using a statistically independent but related control sample - a common challenge in particle…

Data Analysis, Statistics and Probability · Physics 2025-04-18 Eli Gendreau-Distler , Luc Le Pottier , Haichen Wang

Visually-guided acoustic highlighting seeks to rebalance audio in alignment with the accompanying video, creating a coherent audio-visual experience. While visual saliency and enhancement have been widely studied, acoustic highlighting…

Audio and Speech Processing · Electrical Eng. & Systems 2026-02-05 Hugo Malard , Gael Le Lan , Daniel Wong , David Lou Alon , Yi-Chiao Wu , Sanjeel Parekh

Standard flow matching scales well but typically relies on an unstructured source distribution, limiting its ability to learn interpretable latent structure. Latent-variable models, by contrast, capture structure but often sacrifice…

Machine Learning · Computer Science 2026-05-11 Xavier Sumba , Carles Balsells-Rodas , Yingzhen Li

Matching objectives underpin the success of modern generative models and rely on constructing conditional paths that transform a source distribution into a target distribution. Despite being a fundamental building block, conditional paths…

Flow matching has recently emerged as a powerful framework for continuous-time generative modeling. However, when applied to long-tailed distributions, standard flow matching suffers from majority bias, producing minority modes with low…

Machine Learning · Computer Science 2025-10-01 Hyunsoo Song , Minjung Gim , Jaewoong Choi

High-fidelity Monte Carlo simulations and complex inverse problems, such as mapping smeared experimental observations to ground-truth states, are computationally intensive yet essential for robust data analysis. Conditional Flow Matching…

Machine Learning · Computer Science 2026-04-03 Zeyu Xia , Tyler Kim , Trevor Reed , Judy Fox , Geoffrey Fox , Adam Szczepaniak

Flow-based generative models have recently shown impressive performance for conditional generation tasks, such as text-to-image generation. However, current methods transform a general unimodal noise distribution to a specific mode of the…

Machine Learning · Computer Science 2025-02-14 Noam Issachar , Mohammad Salama , Raanan Fattal , Sagie Benaim
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