  We introduce Invertible Dense Networks (i-DenseNets), a more parameter
efficient alternative to Residual Flows. The method relies on an analysis of
the Lipschitz continuity of the concatenation in DenseNets, where we enforce
invertibility of the network by satisfying the Lipschitz constant. We extend
this method by proposing a learnable concatenation, which not only improves the
model performance but also indicates the importance of the concatenated
representation. Additionally, we introduce the Concatenated LipSwish as
activation function, for which we show how to enforce the Lipschitz condition
and which boosts performance. The new architecture, i-DenseNet, out-performs
Residual Flow and other flow-based models on density estimation evaluated in
bits per dimension, where we utilize an equal parameter budget. Moreover, we
show that the proposed model out-performs Residual Flows when trained as a
hybrid model where the model is both a generative and a discriminative model.
