Minimal-Action Discrete Schrödinger Bridge Matching for Peptide Sequence Design

Generative modeling of peptide sequences requires navigating a discrete and highly constrained space in which many intermediate states are chemically implausible or unstable. Existing discrete diffusion methods rely on reversing fixed corruption processes or following prescribed probability paths, which requires numerous sampling steps and forces generation through low-likelihood regions. We introduce Minimal-action discrete Schrödinger Bridge Matching (MadSBM), a rate-based generative framework for peptide design that formulates generation as a controlled continuous-time Markov process on the amino-acid tokens. To yield probability trajectories that remain near high-likelihood sequence spaces throughout generation, MadSBM 1) defines generation relative to a biologically informed reference process and 2) learns a control field that biases transition rates to produce transport paths from a masked prior to the data distribution. We further introduce objective-guided sampling for MadSBM to expand the design space of therapeutic peptide sequences; to our knowledge, this is the first application of discrete classifier guidance to a Schrödinger bridge-based generative framework.