The paper introduces a novel method for solving the Schrödinger Bridge (SB) problem, which is a promising extension of classic diffusion models and is interconnected with Entropic Optimal Transport (EOT). The authors propose an optimal Schrödinger bridge matching (OSBM) procedure that leverages the optimal parameterization of the diffusion process to recover the SB process in a single bridge matching step. This approach addresses the limitations of existing methods, such as iterative bridge matching procedures and heuristic approximations, which can lead to error accumulation and biased solutions. The OSBM is implemented in a light solver called LightSB-M, which uses a Gaussian mixture parameterization of the adjusted Schrödinger potential. This parameterization allows for efficient sampling from conditional distributions and trajectory sampling without numerical integration. The solver is evaluated on various tasks, including the SB benchmark, single-cell data analysis, and unpaired image translation, demonstrating competitive performance and faster convergence compared to other solvers. The paper also discusses the theoretical connections between the proposed method and existing EOT/SB solvers, showing that the OSBM objective is equivalent to the objective used in Energy-based Models (EBM) and LightSB solvers. The authors highlight the potential impact of their work on advancing computational approaches for SB/EOT tasks and outline future research directions, such as extending the method to more general priors and larger-scale generative modeling tasks.The paper introduces a novel method for solving the Schrödinger Bridge (SB) problem, which is a promising extension of classic diffusion models and is interconnected with Entropic Optimal Transport (EOT). The authors propose an optimal Schrödinger bridge matching (OSBM) procedure that leverages the optimal parameterization of the diffusion process to recover the SB process in a single bridge matching step. This approach addresses the limitations of existing methods, such as iterative bridge matching procedures and heuristic approximations, which can lead to error accumulation and biased solutions. The OSBM is implemented in a light solver called LightSB-M, which uses a Gaussian mixture parameterization of the adjusted Schrödinger potential. This parameterization allows for efficient sampling from conditional distributions and trajectory sampling without numerical integration. The solver is evaluated on various tasks, including the SB benchmark, single-cell data analysis, and unpaired image translation, demonstrating competitive performance and faster convergence compared to other solvers. The paper also discusses the theoretical connections between the proposed method and existing EOT/SB solvers, showing that the OSBM objective is equivalent to the objective used in Energy-based Models (EBM) and LightSB solvers. The authors highlight the potential impact of their work on advancing computational approaches for SB/EOT tasks and outline future research directions, such as extending the method to more general priors and larger-scale generative modeling tasks.