Impact statement: The COT-GAN algorithm introduced in this paper is suitable to generate sequential data, when the real dataset consists of i.i.d. sequences or of stationary time series. It opens up doors to many applications that can benefit from time series synthesis. For example, researchers often do not have access to abundant training data due to privacy concerns, high cost, and data scarcity. This hinders the capability of building accurate predictive models. Ongoing research is aimed at developing a modified COT-GAN algorithm to generate financial time series. The high non-stationarity of financial data requires different features and architectures, whilst causality when measuring distances between sequences remains the crucial tool. The application to market generation is of main interest for the financial and insurance industry, for example in model- independent pricing and hedging, portfolio selection, risk management, and stress testing. In broader scientific research, our approach can be used to estimate from data the parameters of simulation-based models that describe physical processes. These models can be, for instance, differential equations describing neural activities, compartmental models in epidemiology, and chemical reactions involving multiple reagents.