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 ($\textbf{BiFlow}$), 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.

翻译：归一化流（NFs）已被确立为生成建模的一种原则性框架。标准NFs包含前向过程与反向过程：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。典型的NF前向变换受显式可逆性约束，确保反向过程可作为其精确解析逆。TARFlow及其变体的最新进展通过结合Transformer与自回归流，使NF方法重获活力，但也揭示了因果解码作为主要瓶颈的问题。在本工作中，我们提出双向归一化流（$\\textbf{BiFlow}$），该框架无需精确解析逆。BiFlow学习一个近似底层噪声到数据逆映射的反向模型，从而支持更灵活的损失函数与架构设计。在ImageNet上的实验表明，相较于因果解码的对应方法，BiFlow在将采样速度提升高达两个数量级的同时，提高了生成质量。BiFlow在基于NF的方法中取得了最先进的结果，并在单次评估（“1-NFE”）方法中展现出具有竞争力的性能。随着NFs近期取得的积极进展，我们希望本研究能进一步引发对这一经典范式的关注。