We present a variational inference scheme to learn a model that solves the Schrödinger Bridge Problem (SBP). In contrast to previous work, our approach is solver-agnostic and guarantees solutions that respect the prior beyond the first fitting iteration. Having this solution allows us to generate new samples from one of the distributions by first sampling from the other one and then solving the dynamical system. We show that our model is able to learn the transformation between the Gaussian distribution and arbitrary data, as well as learning dynamics that follow a potential function.

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