Normalizing flows (NF) recently gained attention as a way to construct generative networks with exact likelihood calculation out of composable layers. However, NF is restricted to dimension-preserving transformations. Surjection VAE (SurVAE) has been proposed to extend NF to dimension-altering transformations. Such networks are desirable because they are expressive and can be precisely trained. We show that the approaches are a re-invention of PDF projection, which appeared over twenty years earlier and is much further developed.

翻译：归一化流（NF）近期因能够通过可组合层构建具有精确似然计算的生成网络而受到关注。然而，NF局限于保维变换。近年来提出的Surjection VAE（SurVAE）将NF扩展至变维变换。此类网络因兼具表达能力与精确训练能力而备受青睐。我们证明这些方法本质上是对二十余年前出现的PDF投影方法的重新发明，而后者的发展已更为成熟。