We introduce three new generative models for time series. Based on Euler discretization and Wasserstein metrics, they are able to capture time marginal distributions and temporal dynamics. Two of these methods rely on the adaptation of generative adversarial networks (GANs) to time series. Both of them outperform state-of-the-art benchmarks by capturing the underlying temporal structure on synthetic time series. The third algorithm, called Conditional Euler Generator (CEGEN), minimizes a dedicated distance between the transition probability distributions over all time steps. In the context of Ito processes, we provide theoretical guarantees that minimizing this criterion implies accurate estimations of the drift and volatility parameters. We demonstrate empirically that CEGEN outperforms state-of-the-art and GAN generators on both marginal and temporal dynamics metrics. Besides, it identifies accurate correlation structures in high dimension. When few data points are available, we verify the effectiveness of CEGEN, when combined with transfer learning methods on Monte Carlo simulations. Finally, we illustrate the robustness of our method on various real-world datasets.