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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

The flow matching has rapidly become a dominant paradigm in classical generative modeling, offering an efficient way to interpolate between two complex distributions. We extend this idea to the quantum realm and introduce the Quantum Flow…

Quantum Physics · Physics 2026-02-03 Zidong Cui , Pan Zhang , Ying Tang

Deep generative models have recently been applied to physical systems governed by partial differential equations (PDEs), offering scalable simulation and uncertainty-aware inference. However, enforcing physical constraints, such as…

Machine Learning · Computer Science 2025-11-27 Utkarsh Utkarsh , Pengfei Cai , Alan Edelman , Rafael Gomez-Bombarelli , Christopher Vincent Rackauckas

We introduce Coupled Flow Matching (CPFM), a framework that integrates controllable dimensionality reduction and high-fidelity reconstruction. CPFM learns coupled continuous flows for both the high-dimensional data x and the low-dimensional…

Machine Learning · Statistics 2025-10-28 Wenxi Cai , Yuheng Wang , Naichen Shi

Over the several recent years, there has been a boom in development of Flow Matching (FM) methods for generative modeling. One intriguing property pursued by the community is the ability to learn flows with straight trajectories which…

Machine Learning · Statistics 2024-11-11 Nikita Kornilov , Petr Mokrov , Alexander Gasnikov , Alexander Korotin

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 (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…

Computer Vision and Pattern Recognition · Computer Science 2026-03-24 Dayu Wang , Jiaye Yang , Weikang Li , Jiahui Liang , Yang Li

Flow Matching (FM) is an effective framework for training a model to learn a vector field that transports samples from a source distribution to a target distribution. To train the model, early FM methods use random couplings, which often…

Computer Vision and Pattern Recognition · Computer Science 2025-05-30 Yexiong Lin , Yu Yao , Tongliang Liu

The efficient construction of accurate channel knowledge maps (CKMs) is crucial for unleashing the full potential of environment-aware wireless networks, yet it remains a difficult ill-posed problem due to the sparsity of available…

Information Theory · Computer Science 2026-01-13 Ziyu Huang , Yong Zeng , Shen Fu , Xiaoli Xu , Hongyang Du

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…

Machine Learning · Computer Science 2025-11-25 Chenrui Ma , Xi Xiao , Tianyang Wang , Xiao Wang , Yanning Shen

Conditional Flow Matching (CFM) unifies conventional generative paradigms such as diffusion models and flow matching. Interaction Field Matching (IFM) is a newer framework that generalizes Electrostatic Field Matching (EFM) rooted in…

Machine Learning · Computer Science 2026-02-03 Daniil Shlenskii , Alexander Varlamov , Nazar Buzun , Alexander Korotin

High-dimensional count data arise in applications such as single-cell RNA sequencing and neural spike trains, where mapping between distributions across successive batches or time points form critical components of data analysis. The recent…

Machine Learning · Statistics 2026-05-11 Ganchao Wei , John Pearson

This paper proposes a novel method, Explicit Flow Matching (ExFM), for training and analyzing flow-based generative models. ExFM leverages a theoretically grounded loss function, ExFM loss (a tractable form of Flow Matching (FM) loss), to…

Machine Learning · Computer Science 2024-07-03 Gleb Ryzhakov , Svetlana Pavlova , Egor Sevriugov , Ivan Oseledets

Achieving high-fidelity and temporally smooth 3D human motion generation remains a challenge, particularly within resource-constrained environments. We introduce FlowMotion, a novel method leveraging Conditional Flow Matching (CFM).…

Graphics · Computer Science 2025-04-28 Manolo Canales Cuba , Vinícius do Carmo Melício , João Paulo Gois

This study presents a conditional flow matching framework for solving physics-constrained Bayesian inverse problems. In this setting, samples from the joint distribution of inferred variables and measurements are assumed available, while…

Normalizing flows are a class of deep generative models that are especially interesting for modeling probability distributions in physics, where the exact likelihood of flows allows reweighting to known target energy functions and computing…

Machine Learning · Statistics 2023-11-27 Leon Klein , Andreas Krämer , Frank Noé

Unconditional flow-matching trains diffusion models to transport samples from a source distribution to a target distribution by enforcing that the flows between sample pairs are unique. However, in conditional settings (e.g.,…

Computer Vision and Pattern Recognition · Computer Science 2025-06-06 George Stoica , Vivek Ramanujan , Xiang Fan , Ali Farhadi , Ranjay Krishna , Judy Hoffman

Flow models parameterized as time-dependent velocity fields can generate data from noise by integrating an ODE. These models are often trained using flow matching, i.e. by sampling random pairs of noise and target points…

Machine Learning · Computer Science 2026-01-26 Alireza Mousavi-Hosseini , Stephen Y. Zhang , Michal Klein , Marco Cuturi

Flow Matching (FM) is a simulation-free method for learning a continuous and invertible flow to interpolate between two distributions, and in particular to generate data from noise. Inspired by the variational nature of the diffusion…

Machine Learning · Statistics 2025-07-14 Chen Xu , Xiuyuan Cheng , Yao Xie

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