Normalizing Flows 的变体与松弛
Variations and Relaxations of Normalizing Flows
AI总结：
本综述探讨了结合 VAEs 和 score-based diffusion 等方法来放宽 Normalizing Flows 严格双射性约束的研究，以解决其维度限制和质量泄漏问题，从而在表达能力、训练速度、样本效率和似然 tractability 间取得平衡。
摘要：
Normalizing Flows (NFs) 描述了一类模型，它们将复杂的目标分布表示为对较简单的基础分布进行一系列双射变换的组合。通过将候选变换的空间限制为微分同胚，NFs 具备高效的精确采样和密度评估能力，使其能够灵活地兼作判别式和生成式模型。然而，对微分同胚的限制要求输入、输出及所有中间空间共享相同维度，限制了其有效表示具有复杂拓扑结构的目标分布的能力。此外，在先验分布与目标分布不同胚的情况下，Normalizing Flows 可能会将质量泄漏到目标分布的支撑集之外。本综述涵盖了一系列近期的研究，这些工作结合了其他生成模型类别（如 VAEs 和 score-based diffusion）的特性，从而放宽了 NFs 严格的双射性约束，以在表达能力、训练速度、样本效率和似然 tractability 之间取得平衡。
英文摘要：
Normalizing Flows (NFs) describe a class of models that express a complex target distribution as the composition of a series of bijective transformations over a simpler base distribution. By limiting the space of candidate transformations to diffeomorphisms, NFs enjoy efficient, exact sampling and density evaluation, enabling NFs to flexibly behave as both discriminative and generative models. Their restriction to diffeomorphisms, however, enforces that input, output and all intermediary spaces share the same dimension, limiting their ability to effectively represent target distributions with complex topologies. Additionally, in cases where the prior and target distributions are not homeomorphic, Normalizing Flows can leak mass outside of the support of the target. This survey covers a selection of recent works that combine aspects of other generative model classes, such as VAEs and score-based diffusion, and in doing so loosen the strict bijectivity constraints of NFs to achieve a balance of expressivity, training speed, sample efficiency and likelihood tractability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
