Normalizing Flows

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Overview

Normalizing flows learn reversible transformations from a simple distribution, such as a Gaussian, into a complex one, allowing both samples and exact probability densities to be computed. Common approaches include coupling and autoregressive layers, spline transformations, continuous flows, and structured or conditional flows for tasks such as image generation, Bayesian inference, anomaly detection, and control. Current work also combines flows with compact latent representations, flow matching, and physics-informed models, extending their use in scientific simulation and uncertainty estimation. A central tension is balancing expressive, multimodal models against efficient and stable computation, while ensuring that good likelihoods translate into reliable mode coverage and calibrated uncertainty.

Latest papers

CardsList

73 papers7 papers in the last four weeks, down 12% on the four weeks before. 0.0% of all new papers.

  1. Factorizable Normalizing Flows for parameter-dependent density morphing

    Jun 29, 2026Davide Valsecchi, Mauro Donegà, Rainer WallnyNormalizing FlowsConditional Distribution Estimation

    Institute for Particle Physics and Astrophysics, D-PHYS, ETH Zurich, Zurich, Switzerland

  2. Simplifying Flow Matching Transformations with Low-Rank Mixture Models

    Jun 29, 2026Liam A. Kruse, Houjun Liu, Alexandros E. Tzikas +2Normalizing FlowsFlow-Based Generative Modeling

    Stanford Intelligent Systems Laboratory in the Department of Aeronautics and Astronautics at Stanford University, Stanford, CA 94305, USA · Industrial and Systems Engineering Department at King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, 31261, KSA

  3. DeCoFlow: Structural Decomposition of Normalizing Flows for Continual Anomaly Detection

    Jun 25, 2026Hun Im, Jungi Lee, Subeen Cha +1Normalizing FlowsContinual Anomaly Detection

    Seoul National University, Seoul, Korea

  4. MIMFlow: Integrating Masked Image Modeling with Normalizing Flows for End-to-End Image Generation

    Jun 24, 2026Yang Chen, Xiaowei Xu, Shuai Wang +4Normalizing FlowsImage Generation

    State Key Laboratory for Novel Software Technology, Nanjing University · Alibaba Group · Shanghai AI Lab

  5. The Reverse Telescoping Coordinate System for Positive Definite Matrices: Geometry, Computation, and Generative Modeling

    Jun 13, 2026Anindya BhadraNormalizing FlowsGenerative Modeling

    Department of Statistics, Purdue University

  6. Learning the Universe: Posterior Reliability of Neural Generative Models in High-Dimensional Field-Level Inference of Cosmic Initial Conditions

    Jun 8, 2026Ludvig Doeser, Jens JascheSimulation-Based InferenceNormalizing Flows

    The Oskar Klein Centre, Department of Physics, Stockholm University, AlbaNova University Centre, SE 106 91 Stockholm, Sweden · Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, New York, NY 10010, USA

  7. Active Flow Expansion for Out-of-Distribution Discovery: from Theory to Molecules

    Jun 7, 2026Riccardo De Santi, Bruce Lee, Cristian Perez Jensen +6Synthetic Data PretrainingNormalizing Flows

    ETH Zurich ETH AI Center · University of Pennsylvania · Caltech FutureHouse

  8. Latent Reasoning with Normalizing Flows

    Jun 4, 2026Guancheng Tu, Xiangjun Fu, Suhao Yu +5Normalizing FlowsContinuous Latent Reasoning

    University of Pennsylvania · UC San Diego · Meta

  9. Neural Galerkin Normalizing Flows for Bayesian Inference of Diffusions with Inaccessible Boundaries

    Jun 3, 2026Riccardo Saporiti, Fabio NobileNormalizing FlowsNeural PDE Solvers

    CSQI École Polytechnique Fédérale de Lausanne Lausanne, Switzerland 1015

  10. Non-Vacuous Certification of Transport MCMC via Oscillation-Controlled Normalizing Flows

    May 31, 2026Jun HuMarkov Chain Monte CarloNormalizing Flows

    China Sanya Science and Education Innovation Park, Wuhan University of Technology, Sanya 572025, China · School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan 430070, China

  11. SRC-Flow: Compact Semantic Representations Enable Normalizing Flows for Image Generation

    May 18, 2026Longtao Jiang, Jianmin Bao, Zhendong Wang +4Normalizing FlowsEmbedding Compression

    University of Science and Technology of China · Kling Team, Kuaishou Technology

  12. Operator-Guided Model Reduction for Generative Sampling in Lattice Field Theory

    May 11, 2026Moxian QianFlow MatchingMarkov Chain Monte Carlo

    Johannes Gutenberg University Mainz, 55128 Mainz, Germany

  13. Language Modeling with Hyperspherical Flows

    May 11, 2026Justin Deschenaux, Caglar GulcehreNormalizing FlowsContinuous Normalizing Flows

    EPFL, Lausanne, Switzerland

  14. Normalizing Trajectory Models

    May 8, 2026Jiatao Gu, Tianrong Chen, Ying Shen +3Normalizing FlowsDiffusion Model Distillation

    Apple · UIUC

  15. Expressivity of Bi-Lipschitz Normalizing Flows: A Score-Based Diffusion Perspective

    May 7, 2026Meira Iske, Carola-Bibiane SchönliebNormalizing FlowsDiffusion Models

    Center for Industrial Mathematics, University of Bremen, Bremen, Germany · Department of Theoretical Physics and Applied Mathematics, University of Cambridge, Cambridge, U.K.

  16. Joint Treatment Effect Estimation from Incomplete Healthcare Data: Temporal Causal Normalizing Flows with LLM-driven Evolutionary MNAR Imputation

    May 6, 2026Olivia Jullian Parra, Sara Zoccheddu, David Catalan Cerezo +7Causal Effect EstimationNormalizing Flows

    Department of Mathematical Modeling and Machine Learning University of Zürich Winterthurerstrasse 190, Zürich 8057 · Department of Mathematics ETH Zürich Rämistrasse 101, Zürich 8092 · Epidemiology, Biostatistics & Prevention Institute (EBPI), University of Zürich Hirschengraben 84, Zürich 8001 +2

  17. Robust Conditional Conformal Prediction via Branched Normalizing Flow

    May 3, 2026Rui Xu, Xingyuan Chen, Wenxing Huang +4Distribution Shift RobustnessNormalizing Flows

    Information Hub, The Hong Kong University of Science and Technology (Guangzhou) · The Second Affiliated Hospital of Guangzhou Medical University

  18. Normalizing Flows with Iterative Denoising

    Apr 21, 2026Tianrong Chen, Jiatao Gu, David Berthelot +2Normalizing FlowsAutoregressive Image Generation

    Apple Machine Learning Research.

  19. Neural posterior estimation of the neutrino direction in IceCube using transformer-encoded normalizing flows on the sphere

    Apr 21, 2026R. Abbasi, M. Ackermann, J. Adams +411Normalizing FlowsTransformer

  20. Complex normalizing flows can almost be information Kähler-Ricci flows

    Apr 20, 2026Andrew GracykInformation GeometryNormalizing Flows

    Department of Mathematics, Purdue University, West Lafayette, IN 47907, United States

  21. Lévy-Flow Models: Heavy-Tail-Aware Normalizing Flows for Financial Risk Management

    Mar 31, 2026Rachid DrissiNormalizing FlowsHeavy-Tailed Distributions

  22. Calorimeter Shower Superresolution with Conditional Normalizing Flows: Implementation and Statistical Evaluation

    Mar 26, 2026Andrea CossoHigh-Energy PhysicsImage Super-Resolution

    Università degli Studi di Genova Scuola di Scienze Matematiche, Fisiche e Naturali Laurea Magistrale in Fisica

  23. Motion Semantics Guided Normalizing Flow for Privacy-Preserving Video Anomaly Detection

    Mar 23, 2026Yang Liu, Boan Chen, Yuanyuan Meng +5Video Anomaly DetectionInterpretable Anomaly Detection

    Tongji Univ. · SJTU · Shanghai Creative Studies Institute +4

  24. Neural Galerkin Normalizing Flow for Transition Probability Density Functions of Diffusion Models

    Mar 19, 2026Riccardo Saporiti, Fabio NobileNormalizing FlowsNeural PDE Solvers

    CSQI, École Polytechnique Féderale de Lausanne, Switzerland

  25. Tackling the Sign Problem in the Doped Hubbard Model with Normalizing Flows

    Mar 18, 2026Dominic Schuh, Lena Funcke, Janik Kreit +2Quantum Many-Body PhysicsMarkov Chain Monte Carlo

    Transdisciplinary Research Area (TRA) Matter, University of Bonn, Bonn, Germany · Helmholtz Institute for Radiation and Nuclear Physics (HISKP), University of Bonn, Bonn, Germany · Institute for Advanced Simulation 4 (IAS-4), Forschungszentrum Jülich, Jülich, Germany

  26. Sampling Boltzmann distributions via normalizing flow approximation of transport maps

    Mar 15, 2026Zia Ur Rehman, Gero FrieseckeBoltzmann SamplingNormalizing Flows

    Department of Mathematics, School of Computation, Information and Technology, Technical University of Munich, Boltzmannstrasse 3, 85748 Garching, Germany

  27. Anomaly detection in time-series via inductive biases in the latent space of conditional normalizing flows

    Mar 12, 2026David Baumgartner, Eliezer de Souza da Silva, Iñigo UrteagaNormalizing FlowsLatent Dynamics Modeling

    Department of Computer Science, Norwegian University of Science and Technology, Norway · BCAM — Basque Center for Applied Mathematics, Spain · Department of Informatics Engineering, University of Coimbra, Portugal +2

  28. NFPO: Stabilized Policy Optimization of Normalizing Flow for Robotic Policy Learning

    Mar 12, 2026Diyuan Shi, Yiqi Tang, Zifeng Zhuang +1RL for RoboticsRobotic RL

    Zhejiang University · Westlake University

  29. RC-NF: Robot-Conditioned Normalizing Flow for Real-Time Anomaly Detection in Robotic Manipulation

    Mar 11, 2026Shijie Zhou, Bin Zhu, Jiarui Yang +3Robotic Anomaly DetectionAnomaly Detection

    Institute of Trustworthy Embodied AI, Fudan University · Shanghai Key Laboratory of Multimodal Embodied AI · Singapore Management University

  30. Temporal-Conditioned Normalizing Flows for Multivariate Time Series Anomaly Detection

    Mar 10, 2026David Baumgartner, Helge Langseth, Kenth Engø-Monsen +1Time-Series Anomaly DetectionNormalizing Flows

    Department of Computer Science, Norwegian University of Science and Technology.