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Normalizing Flows (NFs) are a classical family of likelihood-based methods that have received revived attention. Recent efforts such as TARFlow have shown that NFs are capable of achieving promising performance on image modeling tasks,…

Computer Vision and Pattern Recognition · Computer Science 2026-04-23 Tianrong Chen , Jiatao Gu , David Berthelot , Joshua Susskind , Shuangfei Zhai

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

Normalizing Flows (NFs) are widely used in deep generative models for their exact likelihood estimation and efficient sampling. However, they require substantial memory since the latent space matches the input dimension. Multi-scale…

Machine Learning · Computer Science 2025-12-11 Wei Chen , Shian Du , Shigui Li , Delu Zeng , John Paisley

Modeling real-world distributions can often be challenging due to sample data that are subjected to perturbations, e.g., instrumentation errors, or added random noise. Since flow models are typically nonlinear algorithms, they amplify these…

Machine Learning · Computer Science 2022-10-11 Sameera Ramasinghe , Kasun Fernando , Salman Khan , Nick Barnes

Fueled by the expressive power of deep neural networks, normalizing flows have achieved spectacular success in generative modeling, or learning to draw new samples from a distribution given a finite dataset of training samples. Normalizing…

Machine Learning · Computer Science 2023-05-05 Yuehaw Khoo , Michael Lindsey , Hongli Zhao

Stochastic differential equations (SDEs) are well suited to modelling noisy and irregularly sampled time series found in finance, physics, and machine learning. Traditional approaches require costly numerical solvers to sample between…

Machine Learning · Computer Science 2025-10-30 Naoki Kiyohara , Edward Johns , Yingzhen Li

Temporal collaborative filtering (TCF) methods aim at modelling non-static aspects behind recommender systems, such as the dynamics in users' preferences and social trends around items. State-of-the-art TCF methods employ recurrent neural…

Artificial Intelligence · Computer Science 2020-10-14 Esther Rodrigo Bonet , Duc Minh Nguyen , Nikos Deligiannis

Density estimation, a central problem in machine learning, can be performed using Normalizing Flows (NFs). NFs comprise a sequence of invertible transformations, that turn a complex target distribution into a simple one, by exploiting the…

Machine Learning · Computer Science 2024-01-04 Massimiliano Patacchiola , Aliaksandra Shysheya , Katja Hofmann , Richard E. Turner

Normalizing Flows (NFs) are able to model complicated distributions p(y) with strong inter-dimensional correlations and high multimodality by transforming a simple base density p(z) through an invertible neural network under the change of…

Machine Learning · Computer Science 2023-11-14 Christina Winkler , Daniel Worrall , Emiel Hoogeboom , Max Welling

Discrete flow-based models are a recently proposed class of generative models that learn invertible transformations for discrete random variables. Since they do not require data dequantization and maximize an exact likelihood objective,…

Machine Learning · Computer Science 2021-07-27 Alexandra Lindt , Emiel Hoogeboom

In this paper, we propose an approach to effectively accelerating the computation of continuous normalizing flow (CNF), which has been proven to be a powerful tool for the tasks such as variational inference and density estimation. The…

Machine Learning · Computer Science 2021-01-28 Han-Hsien Huang , Mi-Yen Yeh

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

Generating high-quality time series data has emerged as a critical research topic due to its broad utility in supporting downstream time series mining tasks. A major challenge lies in modeling the intrinsic stochasticity of temporal…

Artificial Intelligence · Computer Science 2025-11-20 He Panjing , Cheng Mingyue , Li Li , Zhang XiaoHan

Normalizing flows are a powerful class of generative models for continuous random variables, showing both strong model flexibility and the potential for non-autoregressive generation. These benefits are also desired when modeling discrete…

Machine Learning · Statistics 2019-06-06 Zachary M. Ziegler , Alexander M. Rush

This paper introduces a generative model equivariant to Euclidean symmetries: E(n) Equivariant Normalizing Flows (E-NFs). To construct E-NFs, we take the discriminative E(n) graph neural networks and integrate them as a differential…

Machine Learning · Computer Science 2022-01-17 Victor Garcia Satorras , Emiel Hoogeboom , Fabian B. Fuchs , Ingmar Posner , Max Welling

Recent advancements in generative modeling, particularly diffusion models, have opened new directions for time series modeling, achieving state-of-the-art performance in forecasting and synthesis. However, the reliance of diffusion-based…

Machine Learning · Computer Science 2025-05-13 Marcel Kollovieh , Marten Lienen , David Lüdke , Leo Schwinn , Stephan Günnemann

The interest in deep learning methods for solving traditional signal processing tasks has been steadily growing in the last years. Time delay estimation (TDE) in adverse scenarios is a challenging problem, where classical approaches based…

Audio and Speech Processing · Electrical Eng. & Systems 2020-02-04 Luca Comanducci , Maximo Cobos , Fabio Antonacci , Augusto Sarti

Normalizing Flows (NFs) describe a class of models that express a complex target distribution as the composition of a series of bijective transformations over a simpler base distribution. By limiting the space of candidate transformations…

Machine Learning · Computer Science 2023-09-11 Keegan Kelly , Lorena Piedras , Sukrit Rao , David Roth

Normalizing Flows (NFs) are a class of generative models distinguished by a mathematically invertible architecture, where the forward pass transforms data into a latent space for density estimation, and the reverse pass generates new…

Computer Vision and Pattern Recognition · Computer Science 2025-12-05 Yang Chen , Xiaowei Xu , Shuai Wang , Chenhui Zhu , Ruxue Wen , Xubin Li , Tiezheng Ge , Limin Wang

We present a novel model Graph Neural Stochastic Differential Equations (Graph Neural SDEs). This technique enhances the Graph Neural Ordinary Differential Equations (Graph Neural ODEs) by embedding randomness into data representation using…

Machine Learning · Computer Science 2023-08-25 Richard Bergna , Felix Opolka , Pietro Liò , Jose Miguel Hernandez-Lobato