Generative Modeling by Minimizing the Wasserstein-2 Loss
Read the original on arXiv Machine Learning →This paper introduces a generative model that minimizes the second‑order Wasserstein loss (W₂) by solving a distribution‑dependent ordinary differential equation (ODE) whose dynamics involve the Kantorovich potential of the true data distribution and its current estimate. The authors prove that the time‑marginal laws of this ODE form a gradient flow for the W₂ loss, converging exponentially to the true data distribution, and propose an Euler scheme that recovers this gradient flow in the limit. An algorithm based on this scheme, combined with persistent training, is shown in experiments to outperform Wasserstein GANs in both low‑ and high‑dimensional settings when the level of persistent training is appropriately increased.
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