In this project, we aimed to solve the multi manifold problem of GANs that use IPM metrics as loss function. One of my approaches was to learn tangent space at each point by local PCA and match them using the fact that points in generated manifold and original manifold that are closer should have similar tangent planes. Another approach was based on boosting to increase the weights of generated points not present in original manifold and construct a weighted MMD formulation using those weights. In low dimensional data with multiple independent clusters, IPM GANs give interconnected clusters as output, while weighted MMD has been successful to separate them.
You can find the final thesis report in the Report Link.