Building the Bridge of Schrödinger: A Continuous Entropic Optimal Transport Benchmark

Аннотация

Over the last several years, there has been significant progress in developing neuralsolvers for the Schrödinger Bridge (SB) problem and applying them to generativemodelling. This new research field is justifiably fruitful as it is interconnectedwith the practically well-performing diffusion models and theoretically groundedentropic optimal transport (EOT). Still, the area lacks non-trivial tests allowinga researcher to understand how well the methods solve SB or its equivalentcontinuous EOT problem. We fill this gap and propose a novel way to create pairsof probability distributions for which the ground truth OT solution is known bythe construction. Our methodology is generic and works for a wide range of OTformulations, in particular, it covers the EOT which is equivalent to SB (the maininterest of our study). This development allows us to create continuous benchmarkdistributions with the known EOT and SB solutions on high-dimensional spacessuch as spaces of images. As an illustration, we use these benchmark pairs to testhow well existing neural EOT/SB solvers actually compute the EOT solution. Ourcode for constructing benchmark pairs under different setups is available at:https://github.com/ngushchin/EntropicOTBenchmark