  Generative models are typically trained on grid-like data such as images. As
a result, the size of these models usually scales directly with the underlying
grid resolution. In this paper, we abandon discretized grids and instead
parameterize individual data points by continuous functions. We then build
generative models by learning distributions over such functions. By treating
data points as functions, we can abstract away from the specific type of data
we train on and construct models that scale independently of signal resolution
and dimension. To train our model, we use an adversarial approach with a
discriminator that acts directly on continuous signals. Through experiments on
both images and 3D shapes, we demonstrate that our model can learn rich
distributions of functions independently of data type and resolution.
