  Identifiability, or recovery of the true latent representations from which
the observed data originates, is de facto a fundamental goal of representation
learning. Yet, most deep generative models do not address the question of
identifiability, and thus fail to deliver on the promise of the recovery of the
true latent sources that generate the observations. Recent work proposed
identifiable generative modelling using variational autoencoders (iVAE) with a
theory of identifiability. Due to the intractablity of KL divergence between
variational approximate posterior and the true posterior, however, iVAE has to
maximize the evidence lower bound (ELBO) of the marginal likelihood, leading to
suboptimal solutions in both theory and practice. In contrast, we propose an
identifiable framework for estimating latent representations using a flow-based
model (iFlow). Our approach directly maximizes the marginal likelihood,
allowing for theoretical guarantees on identifiability, thereby dispensing with
variational approximations. We derive its optimization objective in analytical
form, making it possible to train iFlow in an end-to-end manner. Simulations on
synthetic data validate the correctness and effectiveness of our proposed
method and demonstrate its practical advantages over other existing methods.
