mlsanityData to 7 Oct 2026

From optimal transport to generative modeling: the VEGAN cookbook

arXiv 1705.07642 ↗First posted 22 May 2017stat.MLcited by 41

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Abstract (arXiv)

We study unsupervised generative modeling in terms of the optimal transport (OT) problem between true (but unknown) data distribution PX and the latent variable model distribution PG. We show that the OT problem can be equivalently written in terms of probabilistic encoders, which are constrained to match the posterior and prior distributions over the latent space. When relaxed, this constrained optimization problem leads to a penalized optimal transport (POT) objective, which can be efficiently minimized using stochastic gradient descent by sampling from PX and PG. We show that POT for the 2-Wasserstein distance coincides with the objective heuristically employed in adversarial auto-encoders (AAE) (Makhzani et al., 2016), which provides the first theoretical justification for AAEs known to the authors. We also compare POT to other popular techniques like variational auto-encoders (VAE) (Kingma and Welling, 2014). Our theoretical results include (a) a better understanding of the commonly observed blurriness of images generated by VAEs, and (b) establishing duality between Wasserstein GAN (Arjovsky and Bottou, 2017) and POT for the 1-Wasserstein distance.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 May 2017.

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Citing papers per year: 2021: 7; 2022: 10; 2023: 9; 2024: 7; 2025: 7; 2026: 1.

41 papers.

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  1. 2021Don't Generate Me: Training Differentially Private Generative Models with Sinkhorn Divergencecited by 54
  2. 2021Adversarial Intrinsic Motivation for Reinforcement Learningcited by 40
  3. 2023The Monge Gap: A Regularizer to Learn All Transport Mapscited by 32
  4. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  5. 2021Disentangled Recurrent Wasserstein Autoencodercited by 22
  6. 2024Neural Optimal Transport with Lagrangian Costscited by 16
  7. 2022An Optimal Transport Perspective on Unpaired Image Super-Resolutioncited by 12
  8. 2022Bottlenecks CLUB: Unifying Information-Theoretic Trade-offs Among Complexity, Leakage, and Utilitycited by 12
  9. 2022Continual Variational Autoencoder Learning via Online Cooperative Memorizationcited by 12
  10. 2021Scalable Optimal Transport in High Dimensions for Graph Distances, Embedding Alignment, and Morecited by 10
  11. 2022Review of Disentanglement Approaches for Medical Applications -- Towards Solving the Gordian Knot of Generative Models in Healthcarecited by 9
  12. 2022InfoOT: Information Maximizing Optimal Transportcited by 9
29 more
  1. 2024Accelerating Sinkhorn Algorithm with Sparse Newton Iterationscited by 9
  2. 2021InvGAN: Invertible GANscited by 7
  3. 2022Shedding a PAC-Bayesian Light on Adaptive Sliced-Wasserstein Distancescited by 7
  4. 2024A Review of Bayesian Uncertainty Quantification in Deep Probabilistic Image Segmentationcited by 6
  5. 2023Differentially Private Gradient Flow based on the Sliced Wasserstein Distancecited by 4
  6. 2024Imitation from Diverse Behaviors: Wasserstein Quality Diversity Imitation Learning with Single-Step Archive Explorationcited by 4
  7. 2021Bayesian Distributional Policy Gradientscited by 3
  8. 2022Challenges in creative generative models for music: a divergence maximization perspectivecited by 3
  9. 2023Approximation properties of slice-matching operatorscited by 3
  10. 2024A Sinkhorn-type Algorithm for Constrained Optimal Transportcited by 3
  11. 2025Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problemscited by 3
  12. 2023Investigating and Improving Latent Density Segmentation Models for Aleatoric Uncertainty Quantification in Medical Imagingcited by 2
  13. 2024Rapid Review of Generative AI in Smart Medical Applicationscited by 2
  14. 2021Momentum Contrastive Autoencoder: Using Contrastive Learning for Latent Space Distribution Matching in WAEcited by 1
  15. 2025Sparse Partial Optimal Transport via Quadratic Regularizationcited by 1
  16. 2026Learning to Orchestrate Agents under Uncertaintycited by 1
  17. 2022Unified Perspective on Probability Divergence via Maximum Likelihood Density Ratio Estimation: Bridging KL-Divergence and Integral Probability Metricscited by 0
  18. 2022Multisymplectic Formulation of Deep Learning Using Mean--Field Type Control and Nonlinear Stability of Training Algorithmcited by 0
  19. 2022Auto-Encoding Goodness of Fitcited by 0
  20. 2023Wasserstein Auto-encoded MDPs: Formal Verification of Efficiently Distilled RL Policies with Many-sided Guaranteescited by 0
  21. 2023On Certified Generalization in Structured Predictioncited by 0
  22. 2023Joint Distributional Learning via Cramer-Wold Distancecited by 0
  23. 2023Balanced Marginal and Joint Distributional Learning via Mixture Cramer-Wold Distancecited by 0
  24. 2024Sum-of-Squares Programming for Ma-Trudinger-Wang Regularity of Optimal Transport Mapscited by 0
  25. 2025Cloud Model Characteristic Function Auto-Encoder: Integrating Cloud Model Theory with MMD Regularization for Enhanced Generative Modelingcited by 0
  26. 2025CbLDM: A Diffusion Model for recovering nanostructure from atomic pair distribution functioncited by 0
  27. 2025Bispectral OT: Dataset Comparison using Symmetry-Aware Optimal Transportcited by 0
  28. 2025MELCOT: A Hybrid Learning Architecture with Marginal Preservation for Matrix-Valued Regressioncited by 0
  29. 2025Merging without Forgetting: Continual Fusion of Task-Specific Models via Optimal Transportcited by 0