提出融合IPF与IMF的新方法，提升生成模型稳定性与可控性。
Diffusion & Adversarial Schrödinger Bridges via Iterative Proportional Markovian Fitting
- 结合IPF与IMF，构建迭代比例马尔可夫拟合新框架
- 理论证明该方法在多种设置下收敛，提升生成可靠性
- 可灵活调节图像相似性与生成质量，适配具体任务需求
迭代马尔可夫拟合（IMF）通过交替投影到马尔可夫过程空间与互逆类，有效求解薛定谔桥（SB）问题。然而，实际应用中需引入启发式改进——在每轮迭代中交替拟合前向与后向时间扩散过程，以稳定训练并获得可靠结果，例如在无配对域转换中表现优异。本文揭示该改进版本的IMF与基础的迭代比例拟合（IPF）——也称Sinkhorn算法——存在密切关联。我们证明，该启发式修改实质上融合了IMF与IPF，提出统一的迭代比例马尔可夫拟合（IPMF）方法。通过理论与实证分析，建立IPMF在多种设定下的收敛性，为求解SB问题提供统一框架。此外，从实践角度，IPMF支持在图像相似性与生成质量间灵活权衡，为定制化模型提供新机制。
原文摘要 · Abstract (English)
The Iterative Markovian Fitting (IMF) procedure, which iteratively projects onto the space of Markov processes and the reciprocal class, successfully solves the Schrödinger Bridge (SB) problem. However, an efficient practical implementation requires a heuristic modification -- alternating between fitting forward and backward time diffusion at each iteration. This modification is crucial for stabilizing training and achieving reliable results in applications such as unpaired domain translation. Our work reveals a close connection between the modified version of IMF and the Iterative Proportional Fitting (IPF) procedure -- a foundational method for the SB problem, also known as Sinkhorn's algorithm. Specifically, we demonstrate that the heuristic modification of the IMF effectively integrates both IMF and IPF procedures. We refer to this combined approach as the Iterative Proportional Markovian Fitting (IPMF) procedure. Through theoretical and empirical analysis, we establish the convergence of the IPMF procedure under various settings, contributing to developing a unified framework for solving SB problems. Moreover, from a practical standpoint, the IPMF procedure enables a flexible trade-off between image similarity and generation quality, offering a new mechanism for tailoring models to specific tasks.
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