GANs can be great if you want to intentionally mode collapse, e.g. model a subset of the most likely parts of the data distribution. Why might you want to do this? For example, see Taming Transformers and Unleashing Transformers; these hybrids exploit the generative modelling trilemma; they learn a compressed/quantised codebook of image patches using a GAN, each patch being collapsed into a small set of codes, then they model these information-rich codes using a Transformer to capture the full diversity and global structure of the larger image, even though if you zoom right in you may see small mode collapsed artifacts that don’t matter at a perceivable level (repetition of similar looking hairs, dirt etc)… a bit like with JPEG artifacts.

If you look at the review: https://arxiv.org/pdf/2103.04922.pdf in Table 1, you’ll see in the rightmost column GANs don’t have any “NLL” - this stands for the negative log likelihood, or if you like the model’s density fit over the distribution. Other classes of models, like VAEs, only give bounds on the density (approximate densities). Flows and autoregressive token predictors can give exact densities. The discriminator of GAN just estimates if something is real or fake, not estimating true probabilities (densities). Adversarial training can, however, be used for anomaly detection (and works quite well, e.g. GANomoly and successors).