mlsanityData to 14 Oct 2026

Generative Modeling through the Semi-dual Formulation of Unbalanced Optimal Transport

arXiv 2305.14777 ↗First posted 24 May 2023cs.CV cs.LGcited by 41

Not on the map. Why?

Abstract (arXiv)

Optimal Transport (OT) problem investigates a transport map that bridges two distributions while minimizing a given cost function. In this regard, OT between tractable prior distribution and data has been utilized for generative modeling tasks. However, OT-based methods are susceptible to outliers and face optimization challenges during training. In this paper, we propose a novel generative model based on the semi-dual formulation of Unbalanced Optimal Transport (UOT). Unlike OT, UOT relaxes the hard constraint on distribution matching. This approach provides better robustness against outliers, stability during training, and faster convergence. We validate these properties empirically through experiments. Moreover, we study the theoretical upper-bound of divergence between distributions in UOT. Our model outperforms existing OT-based generative models, achieving FID scores of 2.97 on CIFAR-10 and 6.36 on CelebA-HQ-256. The code is available at urlhttps://github.com/Jae-Moo/UOTM.

Key facts. Cited by 41 papers in the map (data through 14 Oct 2026). Builds on 59 of its 84 references that are in the map. First posted on arXiv 24 May 2023.

Builds on

59 of 84 references.

References · 59

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2020Denoising Diffusion Implicit Modelscited by 9,781
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  4. 2022Generative Adversarial Networkscited by 5,627
  5. 2015Rethinking the Inception Architecture for Computer Visioncited by 5,475
  6. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  7. 2014Deep Learning Face Attributes in the Wildcited by 3,693
  8. 2020Taming Transformers for High-Resolution Image Synthesiscited by 3,253
  9. 2017Progressive Growing of GANs for Improved Quality, Stability, and Variationcited by 2,988
  10. 2016Improved Techniques for Training GANscited by 2,970
  11. 2017Improved Training of Wasserstein GANscited by 2,235
  12. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,636
38 more
  1. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,545
  2. 2020Training Generative Adversarial Networks with Limited Datacited by 1,186
  3. 2016Pixel Recurrent Neural Networkscited by 816
  4. 2018Computational Optimal Transportcited by 780
  5. 2018Which Training Methods for GANs do actually Converge?cited by 679
  6. 2020NVAE: A Deep Hierarchical Variational Autoencodercited by 637
  7. 2021Score-based Generative Modeling in Latent Spacecited by 636
  8. 2021Tackling the Generative Learning Trilemma with Denoising Diffusion GANscited by 516
  9. 2015Optimal Transport for Domain Adaptationcited by 463
  10. 2016Input Convex Neural Networkscited by 414
  11. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusioncited by 233
  12. 2019Optimal transport mapping via input convex neural networkscited by 206
  13. 2020Adversarial Latent Autoencoderscited by 155
  14. 2021StyleSwin: Transformer-based GAN for High-resolution Image Generationcited by 152
  15. 2015Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measurescited by 139
  16. 2022Neural Optimal Transportcited by 126
  17. 2021Unbalanced minibatch Optimal Transport; applications to Domain Adaptationcited by 125
  18. 2017Large-Scale Optimal Transport and Mapping Estimationcited by 123
  19. 2020Learning Energy-Based Models by Diffusion Recovery Likelihoodcited by 123
  20. 2017Stabilizing Training of Generative Adversarial Networks through Regularizationcited by 118
  21. 2020VAEBM: A Symbiosis between Variational Autoencoders and Energy-based Modelscited by 104
  22. 2019Wasserstein-2 Generative Networkscited by 97
  23. 2021Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmarkcited by 96
  24. 2019AutoGAN: Neural Architecture Search for Generative Adversarial Networkscited by 94
  25. 2020Robust Optimal Transport with Applications in Generative Modeling and Domain Adaptationcited by 87
  26. 2021Generative Modeling with Optimal Transport Mapscited by 82
  27. 2022Subspace Diffusion Generative Modelscited by 70
  28. 2020A Contrastive Learning Approach for Training Variational Autoencoder Priorscited by 66
  29. 2017On the regularization of Wasserstein GANscited by 65
  30. 2020On Unbalanced Optimal Transport: An Analysis of Sinkhorn Algorithmcited by 61
  31. 2020Dual Contradistinctive Generative Autoencodercited by 58
  32. 2019Sinkhorn Divergences for Unbalanced Optimal Transportcited by 55
  33. 2018On the Convergence and Robustness of Training GANs with Regularized Optimal Transportcited by 51
  34. 2022Unbalanced Optimal Transport, from Theory to Numericscited by 46
  35. 2020Refining Deep Generative Models via Discriminator Gradient Flowcited by 45
  36. 2018Scalable Unbalanced Optimal Transport using Generative Adversarial Networkscited by 42
  37. 2021Unbalanced Optimal Transport through Non-negative Penalized Linear Regressioncited by 31
  38. 2019On Scalable and Efficient Computation of Large Scale Optimal Transportcited by 29

50 most cited of 59 All 59 (JSON)

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 7; 2024: 9; 2025: 7; 2026: 18.

41 papers.

Sort:

By area:

  1. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Stepcited by 78
  2. 2023Unbalancedness in Neural Monge Maps Improves Unpaired Domain Translationcited by 33
  3. 2024Scalable Wasserstein Gradient Flow for Generative Modeling through Unbalanced Optimal Transportcited by 23
  4. 2023Building the Bridge of Schr"odinger: A Continuous Entropic Optimal Transport Benchmarkcited by 19
  5. 2023Light Schr"odinger Bridgecited by 18
  6. 2024Estimating Barycenters of Distributions with Neural Optimal Transportcited by 14
  7. 2024Robust Barycenter Estimation using Semi-Unbalanced Neural Optimal Transportcited by 9
  8. 2025Learning of Population Dynamics: Inverse Optimization Meets JKO Schemecited by 9
  9. 2023Analyzing and Improving Optimal-Transport-based Adversarial Networkscited by 8
  10. 2024A New Robust Partial p-Wasserstein-Based Metric for Comparing Distributionscited by 7
  11. 2024Improving Neural Optimal Transport via Displacement Interpolationcited by 7
  12. 2023Learning Elastic Costs to Shape Monge Displacementscited by 6
29 more
  1. 2023A High-Quality Robust Diffusion Framework for Corrupted Datasetcited by 6
  2. 2025Overcoming Spurious Solutions in Semi-Dual Neural Optimal Transport: A Smoothing Approach for Learning the Optimal Transport Plancited by 6
  3. 2024Scalable Simulation-free Entropic Unbalanced Optimal Transportcited by 5
  4. 2026QUATRO: Query-Adaptive Trust Region Policy Optimization for LLM Fine-tuningcited by 3
  5. 2025A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solverscited by 2
  6. 2026Fast and Large-Scale Unbalanced Optimal Transport via its Semi-Dual and Adaptive Gradient Methodscited by 2
  7. 2026Unlearning for One-Step Generative Models via Unbalanced Optimal Transportcited by 2
  8. 2024Generative Conditional Distributions by Neural (Entropic) Optimal Transportcited by 1
  9. 2024Unsupervised Point Cloud Completion through Unbalanced Optimal Transportcited by 1
  10. 2025Reweighted Flow Matching via Unbalanced OT for Label-free Long-tailed Generationcited by 1
  11. 2025Experts-Guided Unbalanced Optimal Transport for ISP Learning from Unpaired and/or Paired Datacited by 1
  12. 2026Rate-Optimal Noise Annealing in Semi-Dual Neural Optimal Transport: Tangential Identifiability, Off-Manifold Ambiguity, and Guaranteed Recoverycited by 1
  13. 2026Reward-guided Fine-Tuning of One-Step Generative Models via Wasserstein Gradient Flowcited by 1
  14. 2023Safe Screening for Unbalanced Optimal Transportcited by 0
  15. 2025Exploring bidirectional bounds for minimax-training of Energy-based modelscited by 0
  16. 2025Federated Flow Matchingcited by 0
  17. 2026Multivariate Time Series Data Imputation via Distributionally Robust Regularizationcited by 0
  18. 2026Rethinking the Flow-Based Gradual Domain Adaptation: A Semi-Dual Optimal Transport Perspectivecited by 0
  19. 2026Neural Optimal Transport in Hilbert Spaces: Characterizing Spurious Solutions and Gaussian Smoothingcited by 0
  20. 2026Conditional Unbalanced Optimal Transport Maps: An Outlier-Robust Framework for Conditional Generative Modelingcited by 0
  21. 2026Noise-aware few-shot learning through bi-directional multi-view prompt alignmentcited by 0
  22. 2026UOTIP: Unbalanced Optimal Transport Map for Unpaired Inverse Problemscited by 0
  23. 2026A Biconvex Formulation for Stable Transport of Mixture Models with a Unique Solutioncited by 0
  24. 2026Mind the Residual Gap: Probabilistic Downscaling under Real-World Biascited by 0
  25. 2026One-Step Generative Modeling via Unbalanced Optimal Transportcited by 0
  26. 2026Simultaneous Neural Optimal Transportcited by 0
  27. 2026Distributionally Robust Schr"odinger Bridgecited by 0
  28. 2026VDOT++: Unified Few-Step Video Generation via Unbalanced Optimal Transport Distillationcited by 0
  29. 2026Unbalanced W-Flow: Unbalanced Wasserstein Drifting under Finite-Batch Marginal Fluctuationscited by 0