  Generative Adversarial Network(GAN) provides a good generative framework to
produce realistic samples, but suffers from two recognized issues as mode
collapse and unstable training. In this work, we propose to employ explicit
manifold learning as prior to alleviate mode collapse and stabilize training of
GAN. Since the basic assumption of conventional manifold learning fails in case
of sparse and uneven data distribution, we introduce a new target, Minimum
Manifold Coding (MMC), for manifold learning to encourage simple and unfolded
manifold. In essence, MMC is the general case of the shortest Hamiltonian Path
problem and pursues manifold with minimum Riemann volume. Using the
standardized code from MMC as prior, GAN is guaranteed to recover a simple and
unfolded manifold covering all the training data. Our experiments on both the
toy data and real datasets show the effectiveness of MMCGAN in alleviating mode
collapse, stabilizing training, and improving the quality of generated samples.
