This work deals with image generation, two main problems are addressed: (i ) improvements of specific feature extraction while accounting at multiscale levels intrinsic geometric features, and (ii ) equivariance of the network for reducing the complexity and providing a geometric interpretability. We propose a geometric generative model based on an equivariant partial differential equation (PDE) for group convolution neural networks (G-CNNs), so called PDE-G-CNNs, built on morphology operators and generative adversarial networks (GANs). The proposed geometric morphological GAN model, termed as GM-GAN, is obtained thanks to morphological equivariant convolutions in PDE-G-CNNs. GM-GAN is evaluated qualitatively and quantitatively using FID on MNIST and RotoMNIST, preliminary results show noticeable improvements compared classical GAN.