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Real-world data can be multimodal distributed, e.g., data describing the opinion divergence in a community, the interspike interval distribution of neurons, and the oscillators’ natural frequen- cies. Generating multimodal distributed real- world data has become a challenge to existing generative adversarial networks (GANs). For ex- ample, it is often observed that Neural SDEs have only demonstrated successful performance mainly in generating unimodal time series datasets. In this paper, we propose a novel time series gen- erator, named directed chain GANs (DC-GANs), which inserts a time series dataset (called a neigh- borhood process of the directed chain or input) into the drift and diffusion coefficients of the di- rected chain SDEs with distributional constraints. DC-GANs can generate new time series of the same distribution as the neighborhood process, and the neighborhood process will provide the key step in learning and generating multimodal dis- tributed time series. The proposed DC-GANs are examined on four datasets, including two stochas- tic models from social sciences and computa- tional neuroscience, and two real-world datasets on stock prices and energy consumption. To our best knowledge, DC-GANs are the first work that can generate multimodal time series data and con- sistently outperforms state-of-the-art benchmarks with respect to measures of distribution, data sim- ilarity, and predictive ability.