This paper studies stable learning methods for generative models that enable high-quality data generation. Noise injection is commonly used to stabilize learning. However, selecting a suitable noise distribution is challenging. Diffusion-GAN, a recently developed method, addresses this by using the diffusion process with a timestep-dependent discriminator. We investigate Diffusion-GAN and reveal that data scaling is a key component for stable learning and high-quality data generation. Building on our findings, we propose a learning algorithm, Scale-GAN, that uses data scaling and variance-based regularization. Furthermore, we theoretically prove that data scaling controls the bias-variance trade-off of the estimation error bound. As a theoretical extension, we consider GAN with invertible data augmentations. Comparative evaluations on benchmark datasets demonstrate the effectiveness of our method in improving stability and accuracy.