Part of the cleverness of GANs was to have found a way to train a neural network that generates data without explicitly modeling the probability density.
In a stats textbook, when you know that your training data comes from a normal distribution, you can maximize the MLE wrt the parameters, and then use that for sampling. That's basic theory.
In practice, it was very hard to learn a good pdf for experimental data when you had a training set of images. GANs provided a way to bypass this.
Of course, people could have said "hey let's generate samples without maximizing a loglikelihood first", but they didn't know how to do it properly, how to train the network in any other way besides minimizing cross-entropy (which is equivalent to maximizing loglikelihood).
Then GANs actually provided a new loss function that could be trained. Total paradigm shift!
In a stats textbook, when you know that your training data comes from a normal distribution, you can maximize the MLE wrt the parameters, and then use that for sampling. That's basic theory.
In practice, it was very hard to learn a good pdf for experimental data when you had a training set of images. GANs provided a way to bypass this.
Of course, people could have said "hey let's generate samples without maximizing a loglikelihood first", but they didn't know how to do it properly, how to train the network in any other way besides minimizing cross-entropy (which is equivalent to maximizing loglikelihood).
Then GANs actually provided a new loss function that could be trained. Total paradigm shift!