Building the Bridge of Schrödinger: A Continuous Entropic Optimal Transport Benchmark
This work provides a crucial benchmark for researchers in generative modeling and optimal transport, though it is incremental as it fills a gap in testing existing methods rather than introducing new solvers.
The authors tackled the lack of non-trivial tests for neural solvers of the Schrödinger Bridge (SB) and continuous entropic optimal transport (EOT) problems by proposing a novel method to create pairs of probability distributions with known ground truth OT solutions, enabling high-dimensional benchmarks like images.
Over the last several years, there has been significant progress in developing neural solvers for the Schrödinger 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. Our methodology is generic and works for a wide range of OT formulations, in particular, it covers the EOT which is equivalent to SB (the main interest of our study). This development allows us to create continuous benchmark distributions with the known EOT and SB solutions on high-dimensional spaces such as spaces of images. As an illustration, we use these benchmark pairs to test how well existing neural EOT/SB solvers actually compute the EOT solution. Our code for constructing benchmark pairs under different setups is available at: https://github.com/ngushchin/EntropicOTBenchmark.