Latent Traversals in Generative Models as Potential Flows

TL;DR

This paper introduces a novel approach to understanding and manipulating the latent spaces of deep generative models by modeling latent structures as dynamic potential landscapes, enabling more meaningful and disentangled latent traversals.

Contribution

The authors propose modeling latent spaces with learned potential landscapes governed by PDEs, offering a flexible, physics-inspired method for improved disentanglement and structured representation learning.

Findings

Achieves more qualitatively and quantitatively disentangled trajectories than baselines.

Can be integrated as a regularization during training to improve likelihood.

Demonstrates flexible, semantically meaningful latent traversals.

Abstract

Despite the significant recent progress in deep generative models, the underlying structure of their latent spaces is still poorly understood, thereby making the task of performing semantically meaningful latent traversals an open research challenge. Most prior work has aimed to solve this challenge by modeling latent structures linearly, and finding corresponding linear directions which result in `disentangled' generations. In this work, we instead propose to model latent structures with a learned dynamic potential landscape, thereby performing latent traversals as the flow of samples down the landscape's gradient. Inspired by physics, optimal transport, and neuroscience, these potential landscapes are learned as physically realistic partial differential equations, thereby allowing them to flexibly vary over both space and time. To achieve disentanglement, multiple potentials are learned simultaneously, and are constrained by a classifier to be distinct and semantically self-consistent. Experimentally, we demonstrate that our method achieves both more qualitatively and quantitatively disentangled trajectories than state-of-the-art baselines. Further, we demonstrate that our method can be integrated as a regularization term during training, thereby acting as an inductive bias towards the learning of structured representations, ultimately improving model likelihood on similarly structured data.