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.

该研究的主要目的是通过使用学习的动态潜在地形建模潜在空间，以及受物理学和神经科学启发的偏微分方程，实现语义上有意义的潜在遍历，同时在模型训练中通过作为正则化项的方式，提高模型推断的准确性和结构化表示的学习。