This is likely to be the first problem that you encounter when training GANs. Mode collapse happens when the generator finds a particular set of inputs able to fool the discriminator, and it keeps exploiting this failure case and collapsing lots of values from the latent Z space to the same value.

One solution for this problem is to use "Minibatches-features" or "Unrolled Gans", or just stop training entirely and start again when the generator starts to create a very narrow distribution of outputs: