将流模型视为概率空间中的迭代算法，打通理论与应用的桥梁。
Flow-based generative models as iterative algorithms in probability space
- 用常微分方程建模可逆变换，实现精确密度估计
- 结合Wasserstein度量与梯度流，提供收敛性保证
- 适合想深入理解生成模型理论的研究者
生成式人工智能（GenAI）通过高维数据合成，在图像生成、语言建模、生物信号处理和异常检测等领域带来变革。流模型提供强大框架以捕捉复杂概率分布，具备精确似然估计、高效采样及确定性分布变换能力。该模型基于由常微分方程（ODEs）控制的可逆映射，实现精准密度估计与似然评估。本文以直观数学框架阐述流模型，将其表示为神经网络驱动的连续概率密度。我们探讨关键理论原理，包括Wasserstein度量、梯度流及由ODE支配的概率密度演化，建立收敛性保障，并连接经验进展与理论洞察。通过严谨且易懂的分析，旨在为研究人员与实践者提供在信号处理与机器学习中有效应用流模型的工具。
原文摘要 · Abstract (English)
Generative AI (GenAI) has revolutionized data-driven modeling by enabling the synthesis of high-dimensional data across various applications, including image generation, language modeling, biomedical signal processing, and anomaly detection. Flow-based generative models provide a powerful framework for capturing complex probability distributions, offering exact likelihood estimation, efficient sampling, and deterministic transformations between distributions. These models leverage invertible mappings governed by Ordinary Differential Equations (ODEs), enabling precise density estimation and likelihood evaluation. This tutorial presents an intuitive mathematical framework for flow-based generative models, formulating them as neural network-based representations of continuous probability densities. We explore key theoretical principles, including the Wasserstein metric, gradient flows, and density evolution governed by ODEs, to establish convergence guarantees and bridge empirical advancements with theoretical insights. By providing a rigorous yet accessible treatment, we aim to equip researchers and practitioners with the necessary tools to effectively apply flow-based generative models in signal processing and machine learning.
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