paper-conference

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.

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.

This paper introduces a benchmark for the Schrödinger bridge problem on discrete spaces, providing pairs of distributions with known solutions to enable rigorous evaluation of solvers, and also presents new algorithms as a byproduct.

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.

Interaction Field Matching (IFM) generalizes Electrostatic Field Matching (EFM) by employing general interaction fields, including a quark-inspired solution to modeling challenges of EFM.

iJKOnet combines the JKO scheme with inverse optimization to learn population dynamics without restrictive architectural constraints, achieving better performance than previous JKO-based methods.

RealUID is a universal distillation framework that accelerates all matching models by incorporating real data into the distillation process without the need for GANs.

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