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A common assumption in generative models is that the generator immerses the latent space into a Euclidean ambient space.
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Do GANs learn the distribution? some theory and empirics
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G. Arvanitidis, L. K. Hansen, and S. Hauberg · 2018
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Only bayes should learn a manifold
S. Hauberg · 2018
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Fast approximate geodesics for deep generative models
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Reliable training and estimation of variance networks
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Expected path length on random manifolds
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Learning disconnected manifolds: a no gans land
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