Generative Modeling by Minimizing the Wasserstein-2 Loss
This paper approaches the unsupervised learning problem 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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Asymptotic Guarantees for Learning Generative Models with the Sliced-Wasserstein Distance
Minimum expected distance estimation (MEDE) algorithms have been widely used for probabilistic models with intractable likelihood functions and they have become increasingly popular due to their use in implicit generativ…
Equivalence Between Wasserstein and Value-Aware Loss for Model-based Reinforcement Learning
Learning a generative model is a key component of model-based reinforcement learning. Though learning a good model in the tabular setting is a simple task, learning a useful model in the approximate setting is challengin…
Model-based Reinforcement Learningreinforcement-learningReinforcement LearningReinforcement Learning (RL)Generative model based on minimizing exact empirical Wasserstein distance
Generative Adversarial Networks (GANs) are a very powerful framework for generative modeling. However, they are often hard to train, and learning of GANs often becomes unstable. Wasserstein GAN (WGAN) is a promising fram…
A Unifying View of Variational Generative Wasserstein Flows
Many modern generative models can be viewed as minimizing divergences between probability distributions, yet they rely on different algorithmic and geometric principles. Wasserstein gradient flows provide a continuous-ti…
Y-Diagonal Couplings: Approximating Posteriors with Conditional Wasserstein Distances
In inverse problems, many conditional generative models approximate the posterior measure by minimizing a distance between the joint measure and its learned approximation. While this approach also controls the distance b…