ScooBDoob: Schrödinger Bridge with Doob’s h-Transform for Molecular Dynamics

The slow processes of stochastic dynamical systems can be captured by Molecular Dynamics (MD) simulations, which approximate transition matrices describing how probabilities evolve over metastable conformations. Standard approaches such as Markov State Models (MSMs) extract dominant conformations and transition statistics via eigendecomposition, but face scalability and generalization limits. Here, we introduce Schrödinger Bridge with Doob’s h-Transform (ScooBDoob), a discrete bridge-matching framework that models metastable dynamics by tilting MSM transition rates through Doob’s transform to generate optimal stochastic paths between prescribed initial and terminal ensembles. We demonstrate ScooBDoob’s ability to recover slow processes and generate feasible, target-conditioned trajectories on the Müller-Brown potential and the Aib9 peptide, which folds between two distinct macrostates.