  We introduce new generative models for time series based on Euler
discretization that do not require any pre-stationarization procedure.
Specifically, we develop two GAN based methods, relying on the adaptation of
Wasserstein GANs (Arjovsky et al., 2017) and DVD GANs (Clark et al., 2019b) to
time series. Alternatively, we consider a conditional Euler Generator (CEGEN)
minimizing a distance between the induced conditional densities. In the context
of It\^o processes, we theoretically validate this approach and demonstrate
using the Bures metric that reaching a low loss level provides accurate
estimations for both the drift and the volatility terms of the underlying
process. Tests on simple models show how the Euler discretization and the use
of Wasserstein distance allow the proposed GANs and (more considerably) CEGEN
to outperform state-of-the-art Time Series GAN generation( Yoon et al., 2019b)
on time structure metrics. In higher dimensions we observe that CEGEN manages
to get the correct covariance structures. Finally we illustrate how our model
can be combined to a Monte Carlo simulator in a low data context by using a
transfer learning technique
