mlsanityData to 14 Oct 2026

Potential Flow Generator with L2 Optimal Transport Regularity for Generative Models

arXiv 1908.11462 ↗First posted 29 Aug 2019cs.LG cs.CV stat.MLcited by 31

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Abstract (arXiv)

We propose a potential flow generator with L2 optimal transport regularity, which can be easily integrated into a wide range of generative models including different versions of GANs and flow-based models. We show the correctness and robustness of the potential flow generator in several 2D problems, and illustrate the concept of "proximity" due to the L2 optimal transport regularity. Subsequently, we demonstrate the effectiveness of the potential flow generator in image translation tasks with unpaired training data from the MNIST dataset and the CelebA dataset.

Key facts. Cited by 31 papers in the map (data through 14 Oct 2026). First posted on arXiv 29 Aug 2019.

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Citing papers per year: 2021: 7; 2022: 5; 2023: 8; 2024: 6; 2025: 4; 2026: 1.

31 papers.

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  1. 2022Flow Matching for Generative Modelingcited by 5,702
  2. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  3. 2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 252
  4. 2021An Introduction to Deep Generative Modelingcited by 104
  5. 2022Action Matching: Learning Stochastic Dynamics from Samplescited by 98
  6. 2024PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Lawscited by 31
  7. 2023A mean-field games laboratory for generative modelingcited by 28
  8. 2023Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inferencecited by 20
  9. 2024Dynamical Measure Transport and Neural PDE Solvers for Samplingcited by 20
  10. 2022Taming Hyperparameter Tuning in Continuous Normalizing Flows Using the JKO Schemecited by 17
  11. 2023Gaussian Interpolation Flowscited by 17
  12. 2021Sparse Flows: Pruning Continuous-depth Modelscited by 13
19 more
  1. 2023Flow Factorized Representation Learningcited by 11
  2. 2021Learning High Dimensional Wasserstein Geodesicscited by 10
  3. 2021Jacobian Determinant of Normalizing Flowscited by 8
  4. 2025Optimal Control for Transformer Architectures: Enhancing Generalization, Robustness and Efficiencycited by 8
  5. 2022Neural Lagrangian Schr"odinger Bridge: Diffusion Modeling for Population Dynamicscited by 7
  6. 2023RDA-INR: Riemannian Diffeomorphic Autoencoding via Implicit Neural Representationscited by 7
  7. 2024Differential Equations for Continuous-Time Deep Learningcited by 7
  8. 2025OT-Transformer: A Continuous-time Transformer Architecture with Optimal Transport Regularizationcited by 7
  9. 2022Turning Normalizing Flows into Monge Maps with Geodesic Gaussian Preserving Flowscited by 6
  10. 2023Neural Operator Variational Inference based on Regularized Stein Discrepancy for Deep Gaussian Processescited by 6
  11. 2024Entropy-Informed Weighting Channel Normalizing Flow for Deep Generative Modelscited by 5
  12. 2021Augmented KRnet for density estimation and approximationcited by 4
  13. 2024Combining Wasserstein-1 and Wasserstein-2 proximals: robust manifold learning via well-posed generative flowscited by 4
  14. 2024Conditional Lagrangian Wasserstein Flow for Time Series Imputationcited by 4
  15. 2021Monte Carlo Simulation of SDEs using GANscited by 3
  16. 2023PINF: Continuous Normalizing Flows for Physics-Constrained Deep Learningcited by 1
  17. 2025Neural Hamilton--Jacobi Characteristic Flows for Optimal Transportcited by 1
  18. 2025Dynamical Implicit Neural Representationscited by 0
  19. 2026Implicit Neural Optimal Transport via Fixed-Point Optimizationcited by 0