Normalizing flows, diffusion normalizing flows and variational autoencoders are powerful generative models. In this paper, we provide a unified framework to handle these approaches via Markov chains. Indeed, we consider stochastic normalizing flows as pair of Markov chains fulfilling some properties and show that many state-of-the-art models for data generation fit into this framework. The Markov chains point of view enables us to couple both deterministic layers as invertible neural networks and stochastic layers as Metropolis-Hasting layers, Langevin layers and variational autoencoders in a mathematically sound way. Besides layers with densities as Langevin layers, diffusion layers or variational autoencoders, also layers having no densities as deterministic layers or Metropolis-Hasting layers can be handled. Hence our framework establishes a useful mathematical tool to combine the various approaches.
翻译：流的正常化、 流的传播、 流动的正常化和变异的自动电解器是强大的基因模型。 在本文中, 我们提供了一个统一的框架, 通过 Markov 链处理这些方法。 事实上, 我们把随机的正常化流程视为配对的 Markov 链条中具有某些特性的一对, 并表明许多最先进的数据生成模型都适合这个框架。 Markov 链条观点使我们能够将确定性层作为不可逆的神经网络, 以及像大都会- 豪斯海拔层、 Langevin 层和变异的自动电解码层进行双对齐。 除了朗埃文 层、 扩散层或变异自动电解码层等密度不高的层之外, 我们的框架可以将确定性层与确定性层或大都会- 豪斯海拔层等相匹配。 因此, 我们的框架可以建立一个有用的数学工具, 将各种方法结合起来 。
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