双向归一化流：从数据到噪声的往返映射

摘要

标准化流（Normalizing Flows, NFs）已成为生成建模的理论框架。标准NF由前向过程与反向过程构成：前向过程将数据映射为噪声，而反向过程通过其逆变换生成样本。典型NF的前向变换受显式可逆性约束，确保反向过程能作为其精确解析逆。TARFlow及其变体的最新进展通过结合Transformer与自回归流重振了NF方法，但也暴露出因果解码作为主要瓶颈的问题。本文提出双向标准化流（BiFlow），该框架无需精确解析逆运算。BiFlow通过学习近似底层噪声-数据逆映射的反向模型，实现了更灵活的损失函数与架构设计。在ImageNet上的实验表明，相较于因果解码方案，BiFlow在将采样速度提升最高两个数量级的同时改善了生成质量。该框架在基于NF的方法中取得了最优结果，并在单次评估（"1-NFE"）方法中展现出竞争力。随着NF领域近期取得的鼓舞进展，我们希望本研究能进一步引发对这一经典范式的关注。

English

Normalizing Flows (NFs) have been established as a principled framework for generative modeling. Standard NFs consist of a forward process and a reverse process: the forward process maps data to noise, while the reverse process generates samples by inverting it. Typical NF forward transformations are constrained by explicit invertibility, ensuring that the reverse process can serve as their exact analytic inverse. Recent developments in TARFlow and its variants have revitalized NF methods by combining Transformers and autoregressive flows, but have also exposed causal decoding as a major bottleneck. In this work, we introduce Bidirectional Normalizing Flow (BiFlow), a framework that removes the need for an exact analytic inverse. BiFlow learns a reverse model that approximates the underlying noise-to-data inverse mapping, enabling more flexible loss functions and architectures. Experiments on ImageNet demonstrate that BiFlow, compared to its causal decoding counterpart, improves generation quality while accelerating sampling by up to two orders of magnitude. BiFlow yields state-of-the-art results among NF-based methods and competitive performance among single-evaluation ("1-NFE") methods. Following recent encouraging progress on NFs, we hope our work will draw further attention to this classical paradigm.

双向归一化流：从数据到噪声的往返映射

Bidirectional Normalizing Flow: From Data to Noise and Back

摘要

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