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，但由于其次优的生成质量及缺乏条件建模能力而未被广泛采用。本研究通过两项主要贡献弥补了这一差距。首先，基于一个令人欣喜的观察（即在特定条件下，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），这是SWF的一种简单而有效的扩展，能够实现非参数条件建模。其次，我们借鉴视觉研究中局部连接与多尺度表征的启发，引入两种技术为SWF赋予图像领域合适的归纳偏置，从而大幅提升图像建模的效率与质量。凭借所有改进，我们以纯非参数方式在条件与无条件任务上取得了与众多深度参数化生成模型相媲美的生成性能，充分展现了其巨大潜力。