arXiv:2512.10953v1 Announce Type: new 
Abstract: 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.

يقدم نموذج التدفق العكسي الثنائي (BiFlow) تقدمًا كبيرًا في نمذجة الجيل من خلال القضاء على الحاجة إلى عكس تحليلي دقيق في التدفقات الطبيعية. يتيح هذا الإطار نهجًا أكثر مرونة لتعلم النموذج العكسي، الذي يقارب خريطة الضوضاء إلى البيانات، مما يعزز العملية التوليدية بشكل عام.

La introducción del Bidirectional Normalizing Flow (BiFlow) representa un avance significativo en la modelización generativa al eliminar la necesidad de un inverso analítico exacto en los flujos normalizados. Este marco permite un enfoque más flexible para aprender el modelo inverso, que aproxima la mapeo de ruido a datos, mejorando así el proceso generativo en general.

L'introduction du Bidirectional Normalizing Flow (BiFlow) représente une avancée significative dans la modélisation générative en éliminant la nécessité d'un inverse analytique exact dans les flux normalisants. Ce cadre permet une approche plus flexible pour apprendre le modèle inverse, qui approxime la cartographie du bruit aux données, améliorant ainsi le processus génératif global.

The introduction of Bidirectional Normalizing Flow (BiFlow) presents a significant advancement in generative modeling by eliminating the necessity for an exact analytic inverse in normalizing flows. This framework allows for a more flexible approach to learning the reverse model, which approximates the noise-to-data mapping, enhancing the overall generative process.

Bidirectional Normalizing Flow: From Data to Noise and Back

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