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.

翻译：切片-瓦瑟斯坦流（SWF）是一种有前景的非参数生成建模方法，但由于其生成质量欠佳且缺乏条件建模能力，尚未得到广泛采用。在本工作中，我们做出两大贡献以弥合这一差距。首先，基于一个有利的观察结果（在特定条件下，联合分布的SWF与条件分布的SWF一致），我们提出条件切片-瓦瑟斯坦流（CSWF）——一种简单而有效的SWF扩展，实现了非参数条件建模。其次，我们通过视觉研究中局部连接与多尺度表示启发的两种技术，将图像的恰当归纳偏置引入SWF，极大提升了图像建模的效率与质量。借助上述改进，我们在纯非参数框架下，于条件与非条件任务中均取得了可与众多深度参数生成模型相媲美的生成性能，充分展现了其巨大潜力。