Variations and Relaxations of Normalizing Flows
It provides a synthesis for researchers in generative modeling, but is incremental as it surveys existing methods rather than introducing new ones.
This survey addresses the limitations of Normalizing Flows (NFs), such as their inability to represent complex topologies and mass leakage issues, by reviewing recent works that relax bijectivity constraints through integration with other generative models like VAEs and score-based diffusion.
Normalizing Flows (NFs) describe a class of models that express a complex target distribution as the composition of a series of bijective transformations over a simpler base distribution. By limiting the space of candidate transformations to diffeomorphisms, NFs enjoy efficient, exact sampling and density evaluation, enabling NFs to flexibly behave as both discriminative and generative models. Their restriction to diffeomorphisms, however, enforces that input, output and all intermediary spaces share the same dimension, limiting their ability to effectively represent target distributions with complex topologies. Additionally, in cases where the prior and target distributions are not homeomorphic, Normalizing Flows can leak mass outside of the support of the target. This survey covers a selection of recent works that combine aspects of other generative model classes, such as VAEs and score-based diffusion, and in doing so loosen the strict bijectivity constraints of NFs to achieve a balance of expressivity, training speed, sample efficiency and likelihood tractability.