Generative Modeling by Minimizing the Wasserstein-2 Loss

Abstract:This paper develops a generative model by minimizing the second-order Wasserstein loss (the $W_2$ loss) through a distribution-dependent ordinary differential equation (ODE), whose dynamics involves the Kantorovich potential associated with the true data distribution and a current estimate of it. A main result shows that the time-marginal laws of the ODE form a gradient flow for the $W_2$ loss, which converges exponentially to the true data distribution. An Euler scheme for the ODE is proposed and it is shown to recover the gradient flow for the $W_2$ loss in the limit. An algorithm is designed by following the scheme and applying persistent training, which naturally fits our gradient-flow approach. In both low- and high-dimensional experiments, our algorithm outperforms Wasserstein generative adversarial networks by increasing the level of persistent training appropriately.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2406.13619 [stat.ML]

(or arXiv:2406.13619v5 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2406.13619 Focus to learn more arXiv-issued DOI via DataCite

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