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We introduce manifold-learning flows (M-flows), a new class of generativemodels that simultaneously learn the data manifold as well as a tractableprobability density on that manifold. Combining aspects of normalizing flows,GANs, autoencoders, and energy-based models, they have the potential torepresent datasets with a manifold structure more faithfully and providehandles on dimensionality reduction, denoising, and out-of-distributiondetection. We argue why such models should not be trained by maximum likelihoodalone and present a new training algorithm that separates manifold and densityupdates. In a range of experiments we demonstrate how M-flows learn the datamanifold and allow for better inference than standard flows in the ambient dataspace.

Flows for simultaneous manifold learning and density estimation