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.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| MSC classes: | 34A06, 49Q22, 68T01 |
| Cite as: | arXiv:2406.13619 [stat.ML] |
| (or arXiv:2406.13619v4 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2406.13619 arXiv-issued DOI via DataCite |
Submission history
From: Yu-Jui Huang [view email]
[v1]
Wed, 19 Jun 2024 15:15:00 UTC (318 KB)
[v2]
Sun, 14 Jul 2024 05:54:39 UTC (318 KB)
[v3]
Sun, 28 Dec 2025 21:53:24 UTC (461 KB)
[v4]
Tue, 12 May 2026 21:20:49 UTC (461 KB)