Principled Interpolation in Normalizing Flows

TL;DR

This paper introduces a principled approach to interpolation in normalizing flows by changing the base distributions to Dirichlet and von Mises-Fisher, leading to more meaningful interpolations within the data manifold.

Contribution

It proposes a novel method for interpolation in normalizing flows using manifold-specific base distributions, improving the quality of interpolations without sacrificing generative performance.

Findings

Improved interpolation quality measured by FID and KID scores.

Maintained or enhanced generative performance.

Demonstrated effectiveness on complex data distributions.

Abstract

Generative models based on normalizing flows are very successful in modeling complex data distributions using simpler ones. However, straightforward linear interpolations show unexpected side effects, as interpolation paths lie outside the area where samples are observed. This is caused by the standard choice of Gaussian base distributions and can be seen in the norms of the interpolated samples as they are outside the data manifold. This observation suggests that changing the way of interpolating should generally result in better interpolations, but it is not clear how to do that in an unambiguous way. In this paper, we solve this issue by enforcing a specific manifold and, hence, change the base distribution, to allow for a principled way of interpolation. Specifically, we use the Dirichlet and von Mises-Fisher base distributions on the probability simplex and the hypersphere, respectively. Our experimental results show superior performance in terms of bits per dimension, Fr\'echet Inception Distance (FID), and Kernel Inception Distance (KID) scores for interpolation, while maintaining the generative performance.