In this paper, we present a novel generative adversarial network (GAN) that can describe Markovian temporal dynamics. To generate stochastic sequential data, we introduce a novel stochastic differential equation-based conditional generator and spatial-temporal constrained discriminator networks. To stabilize the learning dynamics of the min-max type of the GAN objective function, we propose well-posed constraint terms for both networks. We also propose a novel conditional Markov Wasserstein distance to induce a pathwise Wasserstein distance. The experimental results demonstrate that our method outperforms state-of-the-art methods using several different types of data.