Principled Interpolation in Normalizing Flows
This work addresses a specific issue in generative modeling for researchers and practitioners using normalizing flows, offering an incremental improvement in interpolation quality.
The paper tackled the problem of poor linear interpolations in normalizing flows, which occur due to Gaussian base distributions causing paths outside the data manifold, by proposing a principled interpolation method using Dirichlet and von Mises-Fisher base distributions on the probability simplex and hypersphere, resulting in superior performance in bits per dimension, FID, and KID scores while maintaining generative performance.
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, Fréchet Inception Distance (FID), and Kernel Inception Distance (KID) scores for interpolation, while maintaining the generative performance.