Generative Modeling by Minimizing the Wasserstein-2 Loss
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917487330721792 |
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| author | Huang, Yu-Jui Malik, Zachariah |
| author_facet | Huang, Yu-Jui Malik, Zachariah |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13619 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generative Modeling by Minimizing the Wasserstein-2 Loss Huang, Yu-Jui Malik, Zachariah Machine Learning 34A06, 49Q22, 68T01 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. |
| title | Generative Modeling by Minimizing the Wasserstein-2 Loss |
| topic | Machine Learning 34A06, 49Q22, 68T01 |
| url | https://arxiv.org/abs/2406.13619 |