Flow Based Models For Manifold Data

Flow-based generative models typically define a latent space with dimensionality identical to the observational space. In many problems, however, the data does not populate the full ambient data-space that they natively reside in, rather inhabiting a lower-dimensional manifold. In such scenarios, flow-based models are unable to represent data structures exactly as their density will always have support off the data manifold, potentially resulting in degradation of model performance. In addition, the requirement for equal latent and data space dimensionality can unnecessarily increase complexity for contemporary flow models. Towards addressing these problems, we propose to learn a manifold prior that affords benefits to both sample generation and representation quality. An auxiliary benefit of our approach is the ability to identify the intrinsic dimension of the data distribution.