There are many NN models that can generate / synthesize images. You could look into Generative Adversarial Networks (GAN), Variational Auto-encoders (VAE), and PixelCNN.

You may check these models.. They have been used so any time for images classifications..

Convolutional Neural Network (CNN)

Deep Beilf Network (DBN)

Dear Radu.

For image recognition, CNN and its variation can be explored. Meanwhile, for image generator, I suggest Generative Adversarial Network(GAN) and its variation are suggested.

Thank you.

Regards

Toto