Diffusion Bridge Mixture Transports, Schr\"odinger Bridge Problems and Generative Modeling

Understand

The dynamic Schr\"odinger bridge problem seeks a stochastic process that defines a transport between two target probability measures, while optimally satisfying the criteria of being closest, in terms of Kullback-Leibler divergence, to a reference process.

• We propose a novel sampling-based iterative algorithm, the iterated diffusion bridge mixture (IDBM) procedure, aimed at solving the dynamic Schr\"odinger bridge problem.
• The IDBM procedure exhibits the attractive property of realizing a valid transport between the target probability measures at each iteration.
• We perform an initial theoretical investigation of the IDBM procedure, establishing its convergence properties.