  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 are agnostic to discretization. To train
our model, we use an adversarial approach with a discriminator that acts on
continuous signals. Through experiments on a wide variety of data modalities
including images, 3D shapes and climate data, we demonstrate that our model can
learn rich distributions of functions independently of data type and
resolution.
