possible to train the generator network even if we don't provide support across all of X space if we make Z be lower dimensional in X then we obtain a low dimensional manifold that assigns no probability whatsoever to most space most points in X space but we're still able to train the model using the discriminator as a guide that's kind of an unusual quirk that sets this framework apart from the methods that are based on maximizing a density function those would break if we evaluated the logarithm of zero density