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Wasserstein-2 Generative Networks

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arxiv 1909.13082 v4 pith:BPGMG4HF submitted 2019-09-28 cs.LG cs.CVstat.ML

Alexander Korotin , Vage Egiazarian , Arip Asadulaev , Alexander Safin , Evgeny Burnaev This is my paper · ORCID
classification cs.LGcs.CVstat.ML
keywords algorithmwasserstein-2cycle-consistencydistancegenerativeimage-to-imagenetworksoptimal
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We propose a novel end-to-end non-minimax algorithm for training optimal transport mappings for the quadratic cost (Wasserstein-2 distance). The algorithm uses input convex neural networks and a cycle-consistency regularization to approximate Wasserstein-2 distance. In contrast to popular entropic and quadratic regularizers, cycle-consistency does not introduce bias and scales well to high dimensions. From the theoretical side, we estimate the properties of the generative mapping fitted by our algorithm. From the practical side, we evaluate our algorithm on a wide range of tasks: image-to-image color transfer, latent space optimal transport, image-to-image style transfer, and domain adaptation.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Constrained Sliced Wasserstein Embedding

    cs.LG 2025-06 conditional novelty 6.0 of 10

    Adding SWGG dissimilarity constraints to sliced Wasserstein embedding, trained via primal-dual optimization with a softsort relaxation, improves pooling accuracy on image, point cloud, and protein-sequence benchmarks.

  2. Computing Optimal Transport Maps and Wasserstein Barycenters Using Conditional Normalizing Flows

    stat.ML 2025-05 conditional novelty 6.0 of 10

    A conditional normalizing flow method that solves the primal optimal transport problem and computes Wasserstein-2 barycenters as weighted averages of maps from a shared latent distribution.

  3. Is In-Context Universality Enough? MLPs are Also Universal In-Context

    stat.ML 2025-02 conditional novelty 6.0 of 10

    MLPs with trainable activations match transformers' in-context universal approximation on permutation-invariant contexts.

  4. DPOT: A DeepParticle method for Computation of Optimal Transport with convergence guarantee

    stat.ML 2025-06 conditional novelty 5.0 of 10

    A simple two-term loss whose minimizer is the Monge map, with a stability bound showing the learned map converges to the optimal transport map as the loss gap shrinks.

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