Flowification: Everything is a Normalizing Flow

TL;DR

This paper introduces flowification, a method to extend neural networks with invertible and likelihood-monitoring capabilities akin to normalizing flows, enabling their use in generative modeling.

Contribution

It demonstrates that neural networks with linear, convolutional, and invertible activation layers can be flowified, broadening the applicability of normalizing flow principles.

Findings

Flowified networks can generate images effectively.

Flowification enables likelihood monitoring in neural networks.

Neural networks with specific layers can be transformed into normalizing flow-like models.

Abstract

The two key characteristics of a normalizing flow is that it is invertible (in particular, dimension preserving) and that it monitors the amount by which it changes the likelihood of data points as samples are propagated along the network. Recently, multiple generalizations of normalizing flows have been introduced that relax these two conditions. On the other hand, neural networks only perform a forward pass on the input, there is neither a notion of an inverse of a neural network nor is there one of its likelihood contribution. In this paper we argue that certain neural network architectures can be enriched with a stochastic inverse pass and that their likelihood contribution can be monitored in a way that they fall under the generalized notion of a normalizing flow mentioned above. We term this enrichment flowification. We prove that neural networks only containing linear layers, convolutional layers and invertible activations such as LeakyReLU can be flowified and evaluate them in the generative setting on image datasets.