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.

On a recent afternoon in Maracaibo, Venezuela, Alexander Marinez, who has short-cropped black hair and three-to-four-day stubble, sat in front of his computer tracking herbiboars in the mushroom forests on Fossil Island. He pressed down on his glowing mouse, the newest addition to his otherwise timeworn gaming setup. The pixelated character on his computer screen followed the tracks of a hedgehoglike creature with triangular tusks and herbs growing out of its back. Outside Marinez's one-story house, the sun bore down on the dirt road. His home lies about six miles away from the strait that connects the Caribbean Sea with Lake Maracaibo, one of the world's richest sources of oil. The character inspected a tunnel. Suddenly, the herbiboar appeared, and the character attacked, stunning it.