Continuous Normalizing Flows

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Continuous normalizing flows use a neural network to define a velocity field that transports samples from a simple distribution, such as Gaussian noise, into data through an ordinary differential equation. Flow matching and optimal-transport paths offer ways to train these dynamics, while likelihood-based training tracks how probability density changes along each trajectory. Researchers adapt the approach with geometric or symmetry-aware models for images, graphs, physical systems, and other structured data, and use it for generation, forecasting, and inverse problems. A central tension is that accurate likelihoods and reliable transports can require costly numerical integration, while high likelihood alone may not ensure that generated samples are semantically correct or robust.

Latest papers

21 papers1 paper in the last four weeks, down 67% on the four weeks before. 0.0% of all new papers.

Seq-Flow: Efficient Probabilistic Forecasting with Self-Rollout Error Control
Oct 7, 2026Yinan Huang, Shitij Govil, Bo Dai +1Probabilistic Forecasting Probabilistic Time Series Forecasting
Georgia Institute of Technology
Off-manifold robustness in synthesizer inversion with joint distribution flow matching
Sep 24, 2026Ben HayesSynthetic-to-Real Domain Adaptation Flow Matching
Sony Computer Science Laboratories Paris
Learning Informative Prior with Infinite-Dimensional Continuous Normalizing Flow for Bayesian Inverse Problem
Sep 3, 2026Yang Zhao, Junxiong Jia, Tao ZhouNormalizing Flows Bayesian Inverse Problems
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China · Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, 100190, China
CQF-HMR: Continuous Quaternion Flows for Probabilistic 3D Human Mesh Recovery from a Single Image
Sep 1, 2026Cuong Le, Bao-Long Tran, Pavlo Melnyk +3Human Mesh Recovery 3D Human Pose Estimation
Linköping University · Independent researcher.
Potential Matching Optimal Transport: Continuous Normalizing Flows for Exact $p$ -Wasserstein Dynamics
Aug 6, 2026Lishuo Zhang, Ruizhi Huang, Yang Yu +1Flow Matching Continuous Normalizing Flows
School of Mathematical Sciences, Shanghai Jiao Tong University · Institute of Natural Sciences, MOE-LSC, Shanghai Jiao Tong University
Joint Flow Matching for Generator-Consistent Classification
Jul 27, 2026Hayden McAlister, Lech SzymanskiFlow Matching Continuous Normalizing Flows
School of Computing University of Otago Dunedin, New Zealand
Stability of Flow Models for Graph Signals
Jul 8, 2026Martin Schmidt, Gonzalo MateosGraph Signal Processing Flow Matching
Dept. of Electrical and Computer Engineering, University of Rochester, Rochester, NY 14627, USA
Self-conditioned Flow Map Language Models via Fixed-point Flows
Jul 1, 2026Jaehoon Yoo, Wonjung Kim, Floor Eijkelboom +4Normalizing Flows One-Step Generative Modeling
KAIST · University of Amsterdam · Carnegie Mellon University
Understanding Latent Flow Models for Tabular Data Synthesis: Targets, Paths, and Sampling
Jun 18, 2026Bahrul Ilmi NasutionSynthetic Tabular Data Generation Continuous Normalizing Flows
Department of Social Statistics, The University of Manchester, UK
Low-Pass Flow Matching
Jun 1, 2026Francesco M. Ruscio, T. Konstantin RuschFlow Matching Image Generation
ELLIS Institute Tübingen & · Max Planck Institute for Intelligent Systems & · AITHYRA +2
Local Diagnostics of Continuous Normalizing Flow for Out-of-Distribution Detection
May 30, 2026Xinwei Cao, Mengxuan Lu, Torbjørn Svendsen +1Speech Processing Distribution Shift Detection
Department of Electronic Systems Norwegian University of Science and Technology Trondheim, Norway · School of Future Technology South China University of Technology Guangzhou, China
Parameter-Efficient Generative Modeling with Controlled Vector Fields
May 27, 2026Peyman MortezaGenerative Modeling Continuous Normalizing Flows
Two-Parameter Flows for Learning Population Dynamics of Physical Systems
May 25, 2026Paul Schwerdtner, Tobias Blickhan, Benjamin PeherstorferDynamical Systems Continuous Normalizing Flows
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA.
StAD: Stein Amortized Divergence for Fast Likelihoods with Diffusion and Flow
May 15, 2026Gurjeet Jagwani, Stephen Thorp, Sinan Deger +1Continuous Normalizing Flows Flow-Based Generative Modeling
Institute of Astronomy and Kavli Institute for Cosmology, University of Cambridge, Cambridge, UK · Research Computing Services, University of Cambridge, Cambridge, UK · Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, UK +1
Language Modeling with Hyperspherical Flows
May 11, 2026Justin Deschenaux, Caglar GulcehreNormalizing Flows Continuous Normalizing Flows
EPFL, Lausanne, Switzerland
CoreFlow: Low-Rank Matrix Generative Models
Apr 27, 2026Dongze Wu, Linglingzhi Zhu, Yao XieGenerative Modeling Continuous Normalizing Flows
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA
Prior-Fitted Functional Flow: In-Context Generative Models for Pharmacokinetics
Apr 19, 2026César Ojeda, Niklas Hartung, Wilhelm Huisinga +6Probabilistic Time Series Forecasting Healthcare
University of Potsdam, Germany · Technical University Berlin, Germany · Freie Universität Berlin, Germany +2
Boltzmann generators for amorphous particle systems
Dec 18, 2025Louis Grenioux, Leonardo Galliano, Ludovic Berthier +2Boltzmann Sampling Continuous Normalizing Flows
CMAP, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France · Center for Computational Mathematics, Flatiron Institute, New York, NY, USA · Laboratoire de Physique de l’École normale supérieure ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France +2
Autonomous-Flow-Based Generation
Nov 13, 2025Hossein Rouhvarzi, Anastasis KratsiosUniversal Approximation Continuous Normalizing Flows
McMaster University and the Vector Institute Department of Mathematics 1280 Main Street West, Hamilton, Ontario, L8S 4K1, Canada
Generative Flows for Potential Outcomes and Counterfactuals
May 21, 2025Dongze Wu, David I. Inouye, Yao XieCounterfactual Prediction Conditional Average Treatment Effect Estimation
School of Industrial and Systems Engineering Georgia Institute of Technology Atlanta, GA · Elmore Family School of Electrical and Computer Engineering Purdue University West Lafayette, IN
Local Flow Matching Generative Models
Oct 3, 2024Chen Xu, Xiuyuan Cheng, Yao XieFlow Matching Generative Modeling
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology. · Department of Mathematics, Duke University

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Seq-Flow: Efficient Probabilistic Forecasting with Self-Rollout Error Control

Yinan Huang, Shitij Govil, Bo Dai, Pan Li

Georgia Institute of Technology

Probabilistic Forecasting Probabilistic Time Series Forecasting Flow-Based Generative Modeling Continuous Normalizing Flows

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Many scientific forecasting tasks require updating a distribution over future trajectories as new observations arrive. Conventional diffusion and flow models generate each forecast from Gaussian noise, often at the cost of many sampling steps. Warm-start methods reuse earlier predictions to reduce this cost, but their models are not trained to perform the forecast update itself, which can compromise quality under few-step sampling. In this work, we introduce Seq-Flow, a conditional flow model whose ODE transports samples from the previous forecast distribution to the updated one. Because successive forecasts often differ only modestly, this transport starts from an informative distribution and can produce accurate updates with few flow evaluations. Recursive reuse also creates a challenge: errors in one forecast become errors in the initial states of subsequent flows. We address this with self-rollout training, in which a moving average copy of the model generates forecasts that initialize later training updates. Unlike self-forcing methods, which reuse generated outputs as conditioning context, Seq-Flow reuses them as the source of the next flow. Experiments On particle-accelerator beam spill forecasting show Seq-Flow reduces CRPS by 65% under a few-NFE sampling budget, while remaining competitive with strong baselines on fluid-dynamics forecasting tasks. Although trained on self-rollouts of at most four updates, Seq-Flow remains accurate over more than 400 consecutive updates. Our code is available at https://github.com/Graph-COM/Seq-Flow.