Flowification: Everything is a Normalizing Flow
This work addresses the challenge of extending normalizing flow capabilities to standard neural networks, potentially broadening their applicability in generative modeling, though it appears incremental as it builds on existing generalizations of flows.
The paper introduces 'flowification', a method to enrich certain neural network architectures with a stochastic inverse pass and likelihood monitoring, enabling them to function as generalized normalizing flows. It proves that networks with linear, convolutional layers, and invertible activations can be flowified and evaluates them on image datasets in generative tasks.
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.