Manifold learning flows are a class of generative modelling techniques that
assume a low-dimensional manifold description of the data. The embedding of
such manifold into the high-dimensional space of the data is achieved via
learnable invertible transformations. Therefore, once the manifold is properly
aligned via a reconstruction loss, the probability density is tractable on the
manifold and maximum likelihood can be used optimize the network parameters.
Naturally, the lower-dimensional representation of the data requires an
injective-mapping. Recent approaches were able to enforce that density aligns
with the modelled manifold, while efficiently calculating the density
volume-change term when embedding to the higher-dimensional space. However,
unless the injective-mapping is analytically predefined, the learned manifold
is not necessarily an efficient representation of the data. Namely, the latent
dimensions of such models frequently learn an entangled intrinsic basis with
degenerate information being stored in each dimension. Alternatively, if a
locally orthogonal and/or sparse basis is to be learned, here coined canonical
intrinsic basis, it can serve in learning a more compact latent space
representation. Towards this end, we propose a canonical manifold learning flow
method, where a novel optimization objective enforces the transformation matrix
to have few prominent and orthogonal basis functions. Canonical manifold flow
yields a more efficient use of the latent space, automatically generating fewer
prominent and distinct dimensions to represent data, and consequently a better
approximation of target distributions than other manifold flow methods in most
experiments we conducted, resulting in lower FID scores.

通过学习具有少量维度流形的生成建模技术，提出一种新的建模流方法，实现了对数据的高效表示，从而更好地近似目标分布并产生较低的 FID 分数。