Probability density estimation is a classical and well studied problem, but standard density estimation methods have historically lacked the power to model complex and high-dimensional image distributions.   More recent generative models leverage the power of neural networks to implicitly learn and represent probability models over complex images.   We describe methods to extract explicit probability density estimates from GANs, and explore the properties of these image density functions.   We perform sanity check experiments to provide evidence that these probabilities are reasonable.   However, we also show that density functions of natural images are difficult to interpret and thus limited in use.   We study reasons for this lack of interpretability, and suggest that we can get better interpretability by doing density estimation on latent representations of images.  
We examine the relationship between probability density values and image content in non-invertible GANs. The authors try to estimate the probability distribution of the image with the help of GAN and develop a proper approximation to the PDFs in the latent space.