  Generative Adversarial Nets (GANs) and Variational Auto-Encoders (VAEs)
provide impressive image generations from Gaussian white noise, but the
underlying mathematics are not well understood. We compute deep convolutional
network generators by inverting a fixed embedding operator. Therefore, they do
not require to be optimized with a discriminator or an encoder. The embedding
is Lipschitz continuous to deformations so that generators transform linear
interpolations between input white noise vectors into deformations between
output images. This embedding is computed with a wavelet Scattering transform.
Numerical experiments demonstrate that the resulting Scattering generators have
similar properties as GANs or VAEs, without learning a discriminative network
or an encoder.
