Minimal-Action Discrete Schrödinger Bridge Matching for Peptide Sequence Design
This work addresses the challenge of designing therapeutic peptides by providing a method to navigate discrete and constrained sequence spaces more efficiently, though it appears incremental as it builds on existing Schrödinger bridge concepts with novel adaptations for peptides.
The paper tackled the problem of generative modeling for peptide sequence design by introducing Minimal-action discrete Schrödinger Bridge Matching (MadSBM), a rate-based framework that formulates generation as a controlled continuous-time Markov process on an amino-acid edit graph, resulting in probability trajectories that remain near high-likelihood sequence neighborhoods and enabling guidance for functional objectives.
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 and flow-based methods rely on reversing fixed corruption processes or following prescribed probability paths, which can force generation through low-likelihood regions and require countless sampling steps. 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 edit graph. To yield probability trajectories that remain near high-likelihood sequence neighborhoods throughout generation, MadSBM 1) defines generation relative to a biologically informed reference process derived from pre-trained protein language model logits and 2) learns a time-dependent control field that biases transition rates to produce low-action transport paths from a masked prior to the data distribution. We finally introduce guidance to the MadSBM sampling procedure towards a specific functional objective, expanding the design space of therapeutic peptides; to our knowledge, this represents the first-ever application of discrete classifier guidance to Schrödinger bridge-based generative models.