(Conditional) generative adversarial networks (GANs) have had great success in recent years, due to their ability to approximate (conditional) distributions over extremely high-dimensional spaces. However, they are highly unstable and computationally expensive to train, especially in the time series setting. Recently, the use of a key object in rough path theory, called the signature of a path, has been proposed. This is able to convert the min–max formulation given by the (conditional) GAN framework into a classical minimization problem. However, this method is extremely costly in terms of memory, which can sometimes become prohibitive. To overcome this, we propose the use of conditional neural stochastic differential equations, designed to have a constant memory cost as a function of depth, being more memory efficient than traditional deep learning architectures. We empirically test the efficiency of our proposed model against other classical approaches, in terms of both memory cost and computational time, and show that it usually outperforms them according to several metrics.