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Continuous normalizing flows (CNFs) are an attractive generative modeling technique, but they have been held back by limitations in their simulation-based maximum likelihood training. We introduce the generalized conditional flow matching…

Conditional Normalizing Flows (CNFs) are flexible generative models capable of representing complicated distributions with high dimensionality and large interdimensional correlations, making them appealing for structured output learning.…

Computer Vision and Pattern Recognition · Computer Science 2023-09-06 Mohsen Zand , Ali Etemad , Michael Greenspan

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

Generative models excel at synthesizing high-fidelity samples from complex data distributions, but they often violate hard constraints arising from physical laws or task specifications. A common remedy is to project intermediate samples…

Machine Learning · Computer Science 2025-09-30 Jinhao Liang , Yixuan Sun , Anirban Samaddar , Sandeep Madireddy , Ferdinando Fioretto

Continuous normalizing flows (CNFs) are a generative method for learning probability distributions, which is based on ordinary differential equations. This method has shown remarkable empirical success across various applications, including…

Machine Learning · Statistics 2024-04-02 Yuan Gao , Jian Huang , Yuling Jiao , Shurong Zheng

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…

Machine Learning · Computer Science 2026-05-12 Oscar Davis , Anastasiia Filippova , Pierre Ablin , Victor Turrisi , Amitis Shidani , Marco Cuturi , Louis Béthune

Flow matching models have shown great potential in image generation tasks among probabilistic generative models. However, most flow matching models in the literature do not explicitly utilize the underlying clustering structure in the…

Computer Vision and Pattern Recognition · Computer Science 2025-10-09 Anirban Samaddar , Yixuan Sun , Viktor Nilsson , Sandeep Madireddy

Continuous Normalizing Flows (CNFs) have emerged as promising deep generative models for a wide range of tasks thanks to their invertibility and exact likelihood estimation. However, conditioning CNFs on signals of interest for conditional…

Machine Learning · Computer Science 2019-12-10 Tan M. Nguyen , Animesh Garg , Richard G. Baraniuk , Anima Anandkumar

Recent advancement in generative models have demonstrated remarkable performance across various data modalities. Beyond their typical use in data synthesis, these models play a crucial role in distribution matching tasks such as latent…

Machine Learning · Computer Science 2025-08-19 Sagar Shrestha , Rajesh Shrestha , Tri Nguyen , Subash Timilsina

Continuous normalizing flows (CNFs) construct invertible mappings between an arbitrary complex distribution and an isotropic Gaussian distribution using Neural Ordinary Differential Equations (neural ODEs). It has not been tractable on…

Computer Vision and Pattern Recognition · Computer Science 2022-03-29 Shian Du , Yihong Luo , Wei Chen , Jian Xu , Delu Zeng

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

Classifier-free guidance is a key component for enhancing the performance of conditional generative models across diverse tasks. While it has previously demonstrated remarkable improvements for the sample quality, it has only been…

Machine Learning · Computer Science 2023-12-11 Qinqing Zheng , Matt Le , Neta Shaul , Yaron Lipman , Aditya Grover , Ricky T. Q. Chen

Normalizing Flows (NFs) are likelihood-based models for continuous inputs. They have demonstrated promising results on both density estimation and generative modeling tasks, but have received relatively little attention in recent years. In…

Computer Vision and Pattern Recognition · Computer Science 2025-06-09 Shuangfei Zhai , Ruixiang Zhang , Preetum Nakkiran , David Berthelot , Jiatao Gu , Huangjie Zheng , Tianrong Chen , Miguel Angel Bautista , Navdeep Jaitly , Josh Susskind

Conditional Flow Matching (CFM), a simulation-free method for training continuous normalizing flows, provides an efficient alternative to diffusion models for key tasks like image and video generation. The performance of CFM in solving…

Machine Learning · Computer Science 2026-03-17 Aram Davtyan , Leello Tadesse Dadi , Volkan Cevher , Paolo Favaro

Partial observations of continuous time-series dynamics at arbitrary time stamps exist in many disciplines. Fitting this type of data using statistical models with continuous dynamics is not only promising at an intuitive level but also has…

Machine Learning · Computer Science 2021-10-29 Ruizhi Deng , Marcus A. Brubaker , Greg Mori , Andreas M. Lehrmann

Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative…

Machine Learning · Statistics 2025-06-10 Grigory Bartosh , Dmitry Vetrov , Christian A. Naesseth

We tackle the problem of sampling from intractable high-dimensional density functions, a fundamental task that often appears in machine learning and statistics. We extend recent sampling-based approaches that leverage controlled stochastic…

Machine Learning · Computer Science 2024-03-12 Dinghuai Zhang , Ricky T. Q. Chen , Cheng-Hao Liu , Aaron Courville , Yoshua Bengio

In this paper, we propose Continuous Graph Flow, a generative continuous flow based method that aims to model complex distributions of graph-structured data. Once learned, the model can be applied to an arbitrary graph, defining a…

Machine Learning · Computer Science 2019-10-01 Zhiwei Deng , Megha Nawhal , Lili Meng , Greg Mori

Continuous Normalizing Flows (CNFs) enable elegant generative modeling but remain bottlenecked by slow sampling: producing a single sample requires solving a nonlinear ODE with hundreds of function evaluations. Recent approaches such as…

Machine Learning · Computer Science 2025-10-23 Erkan Turan , Aristotelis Siozopoulos , Louis Martinez , Julien Gaubil , Emery Pierson , Maks Ovsjanikov

The efficient resolution of Bayesian inverse problems remains challenging due to the high computational cost of traditional sampling methods. In this paper, we propose a novel framework that integrates Conditional Flow Matching (CFM) with a…

Machine Learning · Computer Science 2025-05-20 Daniil Sherki , Ivan Oseledets , Ekaterina Muravleva
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