Dimensionality Reduction Flows

Deep generative modelling using flows has gained popularity owing to the tractable exact log-likelihood estimation with efficient training and synthesis process. Trained flow models carry rich information about the structure and local variance in input data. However, a bottleneck for flow models to scale with increasing dimensions is that the latent space has same size as the high-dimensional input space. In this paper, we propose methods to reduce the latent space dimension of flow models. Our first approach includes replacing standard high dimensional prior with a learned prior from a low dimensional noise space. Further improving to achieve exact log-likelihood with reduced dimensionality, our second approach presents an improved multi-scale architecture (Dinh et al., 2016) via likelihood contribution based factorization of dimensions. Using our method over state-of-the-art flow models, we demonstrate improvements in log-likelihood score on standard image benchmarks. Our work ventures a data dependent factorization scheme which is more efficient than static counterparts in prior works.