Schr\"odinger Bridge

The Schrödinger bridge problem addresses the challenge of finding the most likely stochastic process connecting two probability distributions, minimizing the deviation from a reference process while satisfying endpoint constraints. Current research focuses on developing efficient algorithms, such as iterative Markovian fitting and coupled bridge matching, often implemented with neural networks, to solve this problem for high-dimensional data and diverse applications. This framework finds increasing use in various fields, including generative modeling, inverse problems, and the analysis of complex systems where only snapshots of population-level data are available, offering a powerful tool for data-driven inference and modeling of dynamic processes.