Categorical Schrödinger Bridge Matching

• URL: http://arxiv.org/abs/2502.01416v1
• Date: Mon, 03 Feb 2025 14:55:28 GMT
• Title: Categorical Schrödinger Bridge Matching
• Authors: Grigoriy Ksenofontov, Alexander Korotin,
• Abstract summary: The Schr"odinger Bridge (SB) is a powerful framework for solving generative modeling tasks such as unpaired domain translation. We provide a theoretical and algorithmic foundation for solving SB in discrete spaces using the recently introduced Iterative Markovian Fitting (IMF) procedure. This enables us to develop a practical computational algorithm for SB which we call Categorical Schr"odinger Bridge Matching (CSBM)
• Score: 58.760054965084656
• License:
• Abstract: The Schr\"odinger Bridge (SB) is a powerful framework for solving generative modeling tasks such as unpaired domain translation. Most SB-related research focuses on continuous data space $\mathbb{R}^{D}$ and leaves open theoretical and algorithmic questions about applying SB methods to discrete data, e.g, on finite spaces $\mathbb{S}^{D}$. Notable examples of such sets $\mathbb{S}$ are codebooks of vector-quantized (VQ) representations of modern autoencoders, tokens in texts, categories of atoms in molecules, etc. In this paper, we provide a theoretical and algorithmic foundation for solving SB in discrete spaces using the recently introduced Iterative Markovian Fitting (IMF) procedure. Specifically, we theoretically justify the convergence of discrete-time IMF (D-IMF) to SB in discrete spaces. This enables us to develop a practical computational algorithm for SB which we call Categorical Schr\"odinger Bridge Matching (CSBM). We show the performance of CSBM via a series of experiments with synthetic data and VQ representations of images.

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