  Generative Adversarial Networks (GANs) have proven successful for
unsupervised image generation. Several works have extended GANs to image
inpainting by conditioning the generation with parts of the image to be
reconstructed. Despite their success, these methods have limitations in
settings where only a small subset of the image pixels is known beforehand. In
this paper we investigate the effectiveness of conditioning GANs when very few
pixel values are provided. We propose a modelling framework which results in
adding an explicit cost term to the GAN objective function to enforce
pixel-wise conditioning. We investigate the influence of this regularization
term on the quality of the generated images and the fulfillment of the given
pixel constraints. Using the recent PacGAN technique, we ensure that we keep
diversity in the generated samples. Conducted experiments on FashionMNIST show
that the regularization term effectively controls the trade-off between quality
of the generated images and the conditioning. Experimental evaluation on the
CIFAR-10 and CelebA datasets evidences that our method achieves accurate
results both visually and quantitatively in term of Fr\'echet Inception
Distance, while still enforcing the pixel conditioning. We also evaluate our
method on a texture image generation task using fully-convolutional networks.
As a final contribution, we apply the method to a classical geological
simulation application.
