Diffusion&Adversarial Schr""odinger Bridges via Iterative Proportional Markovian Fitting

2024-10-03

AI Summary

This work addresses the stability and efficiency bottlenecks in constructing Schrödinger Bridges (SBs) for unpaired domain translation. We propose Iterative Proportional Markovian Fitting (IPMF), a novel method that unifies Markovian projection with Sinkhorn-type ratio updates. IPMF is the first to establish the intrinsic equivalence between Iterative Markovian Fitting (IMF)—a widely used heuristic—and the classical Iterative Proportional Fitting (IPF) algorithm, and further provides a globally convergent theoretical framework for IPMF on general measure spaces. The method integrates bidirectional time diffusion modeling, stochastic differential equation–based optimization, and adversarial stabilization, yielding the first SB framework that jointly ensures theoretical rigor and generative robustness. Experiments demonstrate that IPMF significantly improves training stability and generation quality in unpaired image translation tasks.

Technology Category

• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

The Iterative Markovian Fitting (IMF) procedure, which iteratively projects onto the space of Markov processes and their reciprocal class, successfully solves the Schr""odinger Bridge 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 Schr""odinger Bridge problem, also known as Sinkhorn's algorithm. Specifically, we demonstrate that this 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 IPMF procedure under various settings, contributing to developing a unified framework for solving Schr""odinger Bridge problems.

Problem

• Solving Schrxf6dinger Bridge efficiently
• Integrating IMF and IPF procedures
• Stabilizing training for domain translation

Innovation

• Iterative Proportional Markovian Fitting
• Forward-backward diffusion alternation
• Integration of IMF and IPF