  We propose a manifold matching approach to generative models which includes a
distribution generator (or data generator) and a metric generator. In our
framework, we view the real data set as some manifold embedded in a
high-dimensional Euclidean space. The distribution generator aims at generating
samples that follow some distribution condensed around the real data manifold.
It is achieved by matching two sets of points using their geometric shape
descriptors, such as centroid and $p$-diameter, with learned distance metric;
the metric generator utilizes both real data and generated samples to learn a
distance metric which is close to some intrinsic geodesic distance on the real
data manifold. The produced distance metric is further used for manifold
matching. The two networks are learned simultaneously during the training
process. We apply the approach on both unsupervised and supervised learning
tasks: in unconditional image generation task, the proposed method obtains
competitive results compared with existing generative models; in
super-resolution task, we incorporate the framework in perception-based models
and improve visual qualities by producing samples with more natural textures.
Experiments and analysis demonstrate the feasibility and effectiveness of the
proposed framework.
