  Generative modeling has evolved to a notable field of machine learning. Deep
polynomial neural networks (PNNs) have demonstrated impressive results in
unsupervised image generation, where the task is to map an input vector (i.e.,
noise) to a synthesized image. However, the success of PNNs has not been
replicated in conditional generation tasks, such as super-resolution. Existing
PNNs focus on single-variable polynomial expansions which do not fare well to
two-variable inputs, i.e., the noise variable and the conditional variable. In
this work, we introduce a general framework, called CoPE, that enables a
polynomial expansion of two input variables and captures their auto- and
cross-correlations. We exhibit how CoPE can be trivially augmented to accept an
arbitrary number of input variables. CoPE is evaluated in five tasks
(class-conditional generation, inverse problems, edges-to-image translation,
image-to-image translation, attribute-guided generation) involving eight
datasets. The thorough evaluation suggests that CoPE can be useful for tackling
diverse conditional generation tasks.
