Do I have to use neural networks in a generative adversarial network?

I’ve only seen examples that use (various types of) neural networks for both the discriminative and generative model. Is it not sound to use say, a logistic regression model for the discriminative model instead? Do I have to use a neural net instead of say, a clustering algorithm?

Does the “generate novel samples using one technique, then discriminate between novel and original samples using a different technique, then reinforce anything learned that makes discrimination more difficult” general theory behind generative adversarial networks have to be used with neural networks? Or is that just because most uses of GANs today involve image data, which seems to be particularly conducive to neural network analysis?