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Flow-based generative models can be viewed through a physics lens: sampling transports a particle from noise to data by integrating a time-varying velocity field, and each sample corresponds to a trajectory with its own dynamical effort.…

Machine Learning · Computer Science 2026-02-10 Ziyun Li , Huancheng Hu , Soon Hoe Lim , Xuyu Li , Fei Gao , Enmao Diao , Zezhen Ding , Michalis Vazirgiannis , Henrik Bostrom

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…

Machine Learning · Computer Science 2025-12-02 Mudit Gaur , Prashant Trivedi , Shuchin Aeron , Amrit Singh Bedi , George K. Atia , Vaneet Aggarwal

We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for…

Machine Learning · Computer Science 2023-02-09 Yaron Lipman , Ricky T. Q. Chen , Heli Ben-Hamu , Maximilian Nickel , Matt Le

Reconstructing PDE solutions from sparse observations is a core challenge in scientific computing. We present FM4PDE, a flow-matching generative framework that learns the joint distribution of PDE coefficients (or initial states) and…

Machine Learning · Statistics 2026-05-26 Xifeng Zhang , Jin Zhao

Exploring molecular energy landscapes and identifying ground-state conformations are central challenges in computational chemistry. However, generating diverse low-energy conformers from molecular graphs remains expensive with traditional…

Machine Learning · Computer Science 2026-05-25 Guikun Xu , Xiaohan Yi , Ziqiao Meng , Peilin Zhao , Yatao Bian

Flow matching has emerged as a simulation-free alternative to diffusion-based generative modeling, producing samples by solving an ODE whose time-dependent velocity field is learned along an interpolation between a simple source…

Machine Learning · Statistics 2026-04-10 Shivam Kumar , Yixin Wang , Lizhen Lin

Energy-based models for discrete domains, such as graphs, explicitly capture relative likelihoods, naturally enabling composable probabilistic inference tasks like conditional generation or enforcing constraints at test-time. However,…

The design space of discrete-space diffusion or flow generative models are significantly less well-understood than their continuous-space counterparts, with many works focusing only on a simple masked construction. In this work, we aim to…

Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior…

Machine Learning · Computer Science 2024-08-25 Defang Chen , Zhenyu Zhou , Can Wang , Chunhua Shen , Siwei Lyu

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…

Machine Learning · Computer Science 2026-05-06 Zhiqi Li , Duowen Chen , Yuchen Sun , Bo Zhu

We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a…

Machine Learning · Computer Science 2026-01-28 Jan Tauberschmidt , Sophie Fellenz , Sebastian J. Vollmer , Andrew B. Duncan

Diffusion-based generative models have achieved state-of-the-art performance for perceptual quality in speech enhancement (SE). However, their iterative nature requires numerous Neural Function Evaluations (NFEs), posing a challenge for…

Current discriminative depth estimation methods often produce blurry artifacts, while generative approaches suffer from slow sampling due to curvatures in the noise-to-depth transport. Our method addresses these challenges by framing depth…

Computer Vision and Pattern Recognition · Computer Science 2024-12-20 Ming Gui , Johannes Schusterbauer , Ulrich Prestel , Pingchuan Ma , Dmytro Kotovenko , Olga Grebenkova , Stefan Andreas Baumann , Vincent Tao Hu , Björn Ommer

Discovering causal direction from temporal observational data is particularly challenging for symbolic sequences, where functional models and noise assumptions are often unavailable. We propose a novel \emph{Dictionary Based Pattern Entropy…

Machine Learning · Statistics 2026-03-06 Harikrishnan N B , Shubham Bhilare , Aditi Kathpalia , Nithin Nagaraj

Energy based models (EBMs) are appealing for their generality and simplicity in data likelihood modeling, but have conventionally been difficult to train due to the unstable and time-consuming implicit MCMC sampling during contrastive…

Machine Learning · Computer Science 2024-07-23 Junn Yong Loo , Michelle Adeline , Arghya Pal , Vishnu Monn Baskaran , Chee-Ming Ting , Raphael C. -W. Phan

Current state-of-the-art generative models map noise to data distributions by matching flows or scores. A key limitation of these models is their inability to readily integrate available partial observations and additional priors. In…

Modern continuous-time generative models typically induce \emph{V-shaped} flows: each sample travels independently along a nearly straight trajectory from the prior to the data. Although effective, this independent movement overlooks the…

Machine Learning · Computer Science 2026-02-05 Arip Asadulaev , Semyon Semenov , Abduragim Shtanchaev , Eric Moulines , Fakhri Karray , Martin Takac

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

Denoising generative models have recently become the dominant paradigm for dexterous grasp generation, owing to their ability to model complex grasp distributions from large-scale data. However, existing diffusion-based methods typically…

Computer Vision and Pattern Recognition · Computer Science 2026-03-18 Yukun Zhao , Zichen Zhong , Yongshun Gong , Yilong Yin , Haoliang Sun

Simulating transition dynamics between metastable states is a fundamental challenge in dynamical systems and stochastic processes with wide real-world applications in understanding protein folding, chemical reactions and neural activities.…

Machine Learning · Computer Science 2024-10-22 Haibo Wang , Yuxuan Qiu , Yanze Wang , Rob Brekelmans , Yuanqi Du
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