Multi-Marginal Schrödinger Bridge Matching
This addresses trajectory inference for dynamic processes in fields like developmental biology where longitudinal tracking is impossible, representing an incremental extension of existing methods.
The paper tackles the problem of inferring continuous population evolution from discrete temporal snapshots, introducing Multi-Marginal Schrödinger Bridge Matching (MSBM) which shows competitive or superior performance on synthetic and single-cell RNA sequencing data with notable computational efficiency.
Understanding the continuous evolution of populations from discrete temporal snapshots is a critical research challenge, particularly in fields like developmental biology and systems medicine where longitudinal tracking of individual entities is often impossible. Such trajectory inference is vital for unraveling the mechanisms of dynamic processes. While Schrödinger Bridge (SB) offer a potent framework, their traditional application to pairwise time points can be insufficient for systems defined by multiple intermediate snapshots. This paper introduces Multi-Marginal Schrödinger Bridge Matching (MSBM), a novel algorithm specifically designed for the multi-marginal SB problem. MSBM extends iterative Markovian fitting (IMF) to effectively handle multiple marginal constraints. This technique ensures robust enforcement of all intermediate marginals while preserving the continuity of the learned global dynamics across the entire trajectory. Empirical validations on synthetic data and real-world single-cell RNA sequencing datasets demonstrate the competitive or superior performance of MSBM in capturing complex trajectories and respecting intermediate distributions, all with notable computational efficiency.