The paper investigates the training and performance of Generative Adversarial Networks (GANs) using the Maximum Mean Discrepancy (MMD) as a critic, termed MMD GANs. The authors clarify the issue of bias in GAN loss functions, showing that while gradient estimators used in optimization are unbiased, learning a discriminator based on samples leads to biased gradients for the generator parameters. They also discuss the choice of kernel for the MMD critic and characterize the kernel corresponding to the energy distance used in Cramér GANs. The MMD benefits from training strategies developed for Wasserstein GANs, and experiments show that MMD GANs can employ a smaller critic network than Wasserstein GANs, resulting in a simpler and faster-training algorithm with matching performance. The authors propose an improved measure of GAN convergence, the Kernel Inception Distance (KID), and demonstrate how it can be used to dynamically adapt learning rates during GAN training.The paper investigates the training and performance of Generative Adversarial Networks (GANs) using the Maximum Mean Discrepancy (MMD) as a critic, termed MMD GANs. The authors clarify the issue of bias in GAN loss functions, showing that while gradient estimators used in optimization are unbiased, learning a discriminator based on samples leads to biased gradients for the generator parameters. They also discuss the choice of kernel for the MMD critic and characterize the kernel corresponding to the energy distance used in Cramér GANs. The MMD benefits from training strategies developed for Wasserstein GANs, and experiments show that MMD GANs can employ a smaller critic network than Wasserstein GANs, resulting in a simpler and faster-training algorithm with matching performance. The authors propose an improved measure of GAN convergence, the Kernel Inception Distance (KID), and demonstrate how it can be used to dynamically adapt learning rates during GAN training.