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We provide theoretical generalization error bounds for neural network-based Optimal Transport (OT) solvers using minimax approaches, focusing on quadratic OT, and show these bounds depend on standard properties of neural networks, offering a foundation for extending analysis to broader OT formulations.

The paper develops a theoretical and algorithmic foundation for solving the Schrödinger Bridge problem in discrete spaces using Iterative Markovian Fitting, introducing the CSBM algorithm and validating it with experiments on synthetic data and vector-quantized images.

We propose Electrostatic Field Matching (EFM), a novel method inspired by the physics of capacitors, which uses a neural network to learn electrostatic fields for generative modeling and distribution transfer.

We introduce a novel mutual information (MI) estimator leveraging diffusion bridge models, which provides unbiased estimates for challenging data and demonstrates strong performance on standard MI estimation benchmarks.

We introduce a novel distillation technique for diffusion bridge models (DBMs) that significantly accelerates inference (4x to 100x) and improves generation quality by leveraging inverse bridge matching.

We discover that the existing heuristical bi-directional implementation of Iterative Markovian fitting (IMF) procedure for the Schrödinger Bridge problem secretly utilizes the other well-celebrated Iterative Proportional fitting procedure. We analyze such a cross-over of two procedures both theoretically and practically.

We propose a novel light learning algorithm for semi-supervised domain translation which can utilize both paired and unpaired data.

We reveal several limitations of existing solvers for the continuous Gromov-Wasserstein problem and pave the way to get rid of them by proposing a novel solver.