  Many generative models attempt to replicate the density of their input data.
However, this approach is often undesirable, since data density is highly
affected by sampling biases, noise, and artifacts. We propose a method called
SUGAR (Synthesis Using Geometrically Aligned Random-walks) that uses a
diffusion process to learn a manifold geometry from the data. Then, it
generates new points evenly along the manifold by pulling randomly generated
points into its intrinsic structure using a diffusion kernel. SUGAR equalizes
the density along the manifold by selectively generating points in sparse areas
of the manifold. We demonstrate how the approach corrects sampling biases and
artifacts, while also revealing intrinsic patterns (e.g. progression) and
relations in the data. The method is applicable for correcting missing data,
finding hypothetical data points, and learning relationships between data
features.
