Nonlinear Isometric Manifold Learning for Injective Normalizing Flows

Some of the published Normalizing flows are deep generative models approaches assume a dimensionality-reducing (DGM) that represent the probability distribution map to be known and available a priori [12, 13]. of high-dimensional data sets as a change of variables Other works use compositions of manifold learning of a multivariate Gaussian [1, 2]. Using the inverse models and normalizing flows that are trained simultaneously, of this transformation, normalizing flows can e.g., the M-Flow [6], Noisy Injective compute the probability density functions (PDFs) Flows [14], piecewise injective flows called Trumpets explicitly, thus enabling training via the statistically [15], and neural manifold ordinary differential consistent and asymptotically efficient [3] likelihood equations [16].