  Sliced-Wasserstein Flow (SWF) is a promising approach to nonparametric
generative modeling but has not been widely adopted due to its suboptimal
generative quality and lack of conditional modeling capabilities. In this work,
we make two major contributions to bridging this gap. First, based on a
pleasant observation that (under certain conditions) the SWF of joint
distributions coincides with those of conditional distributions, we propose
Conditional Sliced-Wasserstein Flow (CSWF), a simple yet effective extension of
SWF that enables nonparametric conditional modeling. Second, we introduce
appropriate inductive biases of images into SWF with two techniques inspired by
local connectivity and multiscale representation in vision research, which
greatly improve the efficiency and quality of modeling images. With all the
improvements, we achieve generative performance comparable with many deep
parametric generative models on both conditional and unconditional tasks in a
purely nonparametric fashion, demonstrating its great potential.
