Flows for Flows: Training Normalizing Flows Between Arbitrary Distributions with Maximum Likelihood Estimation
This work addresses a limitation in normalizing flows for machine learning practitioners by enabling more flexible mappings, but it is incremental as it builds on existing flow methods.
The paper tackles the problem of training normalizing flows between arbitrary distributions by parameterizing the base density with another normalizing flow, enabling maps with maximum likelihood estimation. It demonstrates utility in conditional flows and introducing optimal transport constraints, showing improved performance in specific cases, though concrete numbers are not provided.
Normalizing flows are constructed from a base distribution with a known density and a diffeomorphism with a tractable Jacobian. The base density of a normalizing flow can be parameterised by a different normalizing flow, thus allowing maps to be found between arbitrary distributions. We demonstrate and explore the utility of this approach and show it is particularly interesting in the case of conditional normalizing flows and for introducing optimal transport constraints on maps that are constructed using normalizing flows.