Generator of generative adversarial networks (GAN) maps latent random variable into data random variable. GAN inversion is mapping data random variable to latent random variable by inverting the generator of GAN. When training the encoder for generator inversion, using the mean squared error causes the encoder to not converge because there is information loss on the latent random variable in the generator. In other words, it is impossible to train an encoder that inverts the generator as it, because the generator may ignore some information of the latent random variable. This paper introduces a dynamic latent scale GAN, a method for training a generator that does not lose information from the latent random variable, and an encoder that inverts the generator. When the latent random variable is an i.i.d. (independent and identically distributed) random variable, dynamic latent scale GAN dynamically scales each element of the latent random variable during GAN training to adjust the entropy of the latent random variable. As training progresses, the entropy of the latent random variable decreases until there is no information loss on the latent random variable in the generator. If there is no information loss on the latent random variable in the generator, the encoder can converge to invert the generator. The scale of the latent random variable depends on the amount of information that the encoder can recover. It can be calculated from the element-wise variance of the predicted latent random variable from the encoder. Since the scale of latent random variable changes dynamically in dynamic latent scale GAN, the encoder should be trained with a generator during GAN training. The encoder can be integrated with the discriminator, and the loss for the encoder is added to the generator loss for fast training. Also, dynamic latent scale GAN can be used for continuous attribute editing with InterFaceGAN.