Normalising flows are statistical models that transform a complex density
into a simpler density through the use of bijective transformations enabling
both density estimation and data generation from a single model. In the context
of image modelling, the predominant choice has been the Glow-based
architecture, whereas alternative architectures remain largely unexplored in
the research community. In this work, we propose a novel architecture called
MixerFlow, based on the MLP-Mixer architecture, further unifying the generative
and discriminative modelling architectures. MixerFlow offers an effective
mechanism for weight sharing for flow-based models. Our results demonstrate
better density estimation on image datasets under a fixed computational budget
and scales well as the image resolution increases, making MixeFlow a powerful
yet simple alternative to the Glow-based architectures. We also show that
MixerFlow provides more informative embeddings than Glow-based architectures.

通过使用双射变换将复杂密度转化为简单密度的统计模型，我们提出了一种名为 MixerFlow 的新型架构，基于 MLP-Mixer 架构，进一步统一生成和判别建模架构。MixerFlow 提供了一种用于流模型的有效权重共享机制，并在固定的计算预算下，在图像数据集上展示了更好的密度估计，随着图像分辨率的增加，缩放效果良好，使 MixerFlow 成为 Glow-based 架构的一个强大而简单的替代方案。我们还显示 MixerFlow 提供比 Glow-based 架构更丰富的嵌入。

图像建模的 MixerFlow

MixerFlow for Image Modelling

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.

通过结合其他生成模型类别的方面，如 VAEs 和基于分数的扩散，放宽了 NFs 的严格双射约束，从而实现了表达能力、训练速度、样本效率和似然可追踪性的平衡。