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Sampling from unnormalized densities is analogous to the generative modeling problem, but the target distribution is defined by a known energy function instead of data samples. Because evaluating the energy function is often costly, a…

Machine Learning · Computer Science 2026-05-06 Aaron Havens , Brian Karrer , Neta Shaul

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 have shown great success as general-purpose density estimators. However, many real world applications require the use of domain-specific knowledge, which normalizing flows cannot readily incorporate. We propose…

Machine Learning · Statistics 2022-03-17 Gianluigi Silvestri , Emily Fertig , Dave Moore , Luca Ambrogioni

We present an alternative to reweighting techniques for modifying distributions to account for a desired change in an underlying conditional distribution, as is often needed to correct for mis-modelling in a simulated sample. We employ…

High Energy Physics - Phenomenology · Physics 2023-05-01 Malte Algren , Tobias Golling , Manuel Guth , Chris Pollard , John Andrew Raine

Normalizing flows are deep generative models that enable efficient likelihood estimation and sampling through invertible transformations. A key challenge is to design linear layers that enhance expressiveness while maintaining efficient…

Machine Learning · Computer Science 2025-11-18 Xuchen Feng , Siyu Liao

Generative modeling seeks to uncover the underlying factors that give rise to observed data that can often be modeled as the natural symmetries that manifest themselves through invariances and equivariances to certain transformation laws.…

Machine Learning · Computer Science 2022-08-16 Avishek Joey Bose , Marcus Brubaker , Ivan Kobyzev

Real-world data with underlying structure, such as pictures of faces, are hypothesized to lie on a low-dimensional manifold. This manifold hypothesis has motivated state-of-the-art generative algorithms that learn low-dimensional data…

Machine Learning · Statistics 2022-04-28 Edmond Cunningham , Renos Zabounidis , Abhinav Agrawal , Madalina Fiterau , Daniel Sheldon

Our universe is homogeneous and isotropic, and its perturbations obey translation and rotation symmetry. In this work we develop Translation and Rotation Equivariant Normalizing Flow (TRENF), a generative Normalizing Flow (NF) model which…

Cosmology and Nongalactic Astrophysics · Physics 2022-08-03 Biwei Dai , Uros Seljak

Reinforcement learning policies are typically represented by black-box neural networks, which are non-interpretable and not well-suited for safety-critical domains. To address both of these issues, we propose constrained normalizing flow…

Machine Learning · Computer Science 2024-05-03 Finn Rietz , Erik Schaffernicht , Stefan Heinrich , Johannes A. Stork

Understanding the dynamics of complex molecular processes is often linked to the study of infrequent transitions between long-lived stable states. The standard approach to the sampling of such rare events is to generate an ensemble of…

Computational Physics · Physics 2023-05-22 Sebastian Falkner , Alessandro Coretti , Salvatore Romano , Phillip Geissler , Christoph Dellago

Flow-based deep generative models learn data distributions by transforming a simple base distribution into a complex distribution via a set of invertible transformations. Due to the invertibility, such models can score unseen data samples…

Machine Learning · Computer Science 2019-06-18 Maximilian Schmidt , Marko Simic

Normalizing flows are a class of machine learning models used to construct a complex distribution through a bijective mapping of a simple base distribution. We demonstrate that normalizing flows are particularly well suited as a Monte Carlo…

Nuclear Theory · Physics 2021-08-11 Jack Brady , Pengsheng Wen , Jeremy W. Holt

Fair representation learning is an attractive approach that promises fairness of downstream predictors by encoding sensitive data. Unfortunately, recent work has shown that strong adversarial predictors can still exhibit unfairness by…

Machine Learning · Computer Science 2022-03-21 Mislav Balunović , Anian Ruoss , Martin Vechev

We propose two new evaluation metrics to assess realness of generated images based on normalizing flows: a simpler and efficient flow-based likelihood distance (FLD) and a more exact dual-flow based likelihood distance (D-FLD). Because…

Computer Vision and Pattern Recognition · Computer Science 2024-10-08 Pranav Jeevan , Neeraj Nixon , Amit Sethi

Foundational language models show a remarkable ability to learn new concepts during inference via context data. However, similar work for images lag behind. To address this challenge, we introduce FLoWN, a flow matching model that learns to…

Machine Learning · Computer Science 2025-04-22 Daniel Saragih , Deyu Cao , Tejas Balaji , Ashwin Santhosh

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

Diffusion-based models decompose sampling into many small Gaussian denoising steps -- an assumption that breaks down when generation is compressed to a few coarse transitions. Existing few-step methods address this through distillation,…

Computer Vision and Pattern Recognition · Computer Science 2026-05-14 Jiatao Gu , Tianrong Chen , Ying Shen , David Berthelot , Shuangfei Zhai , Josh Susskind

We propose a continuous normalizing flow for sampling from the high-dimensional probability distributions of Quantum Field Theories in Physics. In contrast to the deep architectures used so far for this task, our proposal is based on a…

Machine Learning · Computer Science 2021-11-29 Pim de Haan , Corrado Rainone , Miranda C. N. Cheng , Roberto Bondesan

Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations…

Machine Learning · Computer Science 2025-12-02 T. Anderson Keller

Generative adversarial networks (GANs) and normalizing flows are both approaches to density estimation that use deep neural networks to transform samples from an uninformative prior distribution to an approximation of the data distribution.…

Machine Learning · Computer Science 2021-12-15 Tianci Liu , Jeffrey Regier