Symmetrized Schrödinger Bridge Matching
Keywords: schrödinger bridge, probabilistic generative method, stochastic optimal control
TL;DR: we present a symmetrization method for probabilistic diffusion models
Abstract: Schrödinger bridge (SB) has demonstrated numerous applications in probabilistic generative modeling. Finding the solution of probability paths aligns with entropy-regularized optimal transport that employs the Sinkhorn algorithm, which is characterized by performing iterative proportional fitting between marginal densities. This paper argues that the standard training of the SB is prone to exaggerate the amount of learning due to its inherent geometric nature. We leverage a symmetrized variant of Sinkhorn to study more lenient convergence of Schrödinger potentials and prove distinctive theoretical properties of the symmetrization such as linear convergence and monotonic improvements. To this end, we propose a dynamic SB algorithm named Symmetrized Schrödinger Bridge Matching (SSBM). Inspired by score and flow matching models, the concurrent projection scheme of SSBM is conceptualized as matching forward and backward drifts concurrently, constructing a time-symmetric learning objective for the SB model. We empirically validate our SB method by solving classical optimal transportation and model-based stochastic optimal control problems with physical dynamics.
Primary Area: general machine learning (i.e., none of the above)
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Submission Number: 6777
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