This paper introduces a novel generative model for discrete distributions based on continuous normalizing flows on the submanifold of factorizing discrete measures. Integration of the flow gradually assigns categories and avoids issues of discretizing the latent continuous model like rounding, sample truncation etc. General non-factorizing discrete distributions capable of representing complex statistical dependencies of structured discrete data, can be approximated by embedding the submanifold into a the meta-simplex of all joint discrete distributions and data-driven averaging. Efficient training of the generative model is demonstrated by matching the flow of geodesics of factorizing discrete distributions. Various experiments underline the approach's broad applicability.

翻译：本文提出一种新颖的离散分布生成模型，该模型基于因子化离散测度子流形上的连续归一化流。流的积分逐步分配类别，避免了离散化潜在连续模型（如取整、样本截断等）的问题。能够表示结构化离散数据复杂统计依赖的通用非因子化离散分布，可通过将子流形嵌入到所有联合离散分布的元单纯形中并进行数据驱动平均来近似。通过匹配因子化离散分布的测地流，展示了生成模型的高效训练。多项实验验证了该方法广泛的适用性。