  Deep generative modeling using flows has gained popularity owing to the
tractable exact log-likelihood estimation with efficient training and synthesis
process. However, flow models suffer from the challenge of having high
dimensional latent space, the same in dimension as the input space. An
effective solution to the above challenge as proposed by Dinh et al. (2016) is
a multi-scale architecture, which is based on iterative early factorization of
a part of the total dimensions at regular intervals. Prior works on generative
flow models involving a multi-scale architecture perform the dimension
factorization based on static masking. We propose a novel multi-scale
architecture that performs data-dependent factorization to decide which
dimensions should pass through more flow layers. To facilitate the same, we
introduce a heuristic based on the contribution of each dimension to the total
log-likelihood which encodes the importance of the dimensions. Our proposed
heuristic is readily obtained as part of the flow training process, enabling
the versatile implementation of our likelihood contribution based multi-scale
architecture for generic flow models. We present such implementations for
several state-of-the-art flow models and demonstrate improvements in
log-likelihood score and sampling quality on standard image benchmarks. We also
conduct ablation studies to compare the proposed method with other options for
dimension factorization.
