Building the Bridge of Schr\"odinger: A Continuous Entropic Optimal Transport Benchmark

Understand

Over the last several years, there has been significant progress in developing neural solvers for the Schr\"odinger Bridge (SB) problem and applying them to generative modelling.

• This new research field is justifiably fruitful as it is interconnected with the practically well-performing diffusion models and theoretically grounded entropic optimal transport (EOT).
• Still, the area lacks non-trivial tests allowing a researcher to understand how well the methods solve SB or its equivalent continuous EOT problem.
• We fill this gap and propose a novel way to create pairs of probability distributions for which the ground truth OT solution is known by the construction.