The general class of model that you can use to create synthetic data is called a generative model [1]. The style of learning that pits one of these generative models against a discriminative one (the class you can't generate data from, including traditional neural networks) is called adversarial learning [2]. It's worth noting that normally you can use generative models for classification on their own as well.
[1] https://en.wikipedia.org/wiki/Generative_model
[2] https://en.wikipedia.org/wiki/Adversarial_machine_learning