Diffusion Bridge Mixture Transports, Schrödinger Bridge Problems and Generative Modeling

The dynamic Schrödinger 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 Schrödinger 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 …

algorithm bridge diffusion divergence dynamic generative generative modeling iterative modeling novel probability process reference sampling stochastic stochastic process terms transport