  Disentanglement aims to recover meaningful latent ground-truth factors from
the observed distribution solely, and is formalized through the theory of
identifiability. The identifiability of independent latent factors is proven to
be impossible in the unsupervised i.i.d. setting under a general nonlinear map
from factors to observations. In this work, however, we demonstrate that it is
possible to recover quantized latent factors under a generic nonlinear
diffeomorphism. We only assume that the latent factors have independent
discontinuities in their density, without requiring the factors to be
statistically independent. We introduce this novel form of identifiability,
termed quantized factor identifiability, and provide a comprehensive proof of
the recovery of the quantized factors.
