Minimal-Action Discrete Schr\"odinger Bridge Matching for Peptide Sequence Design

TL;DR

This paper introduces MadSBM, a novel discrete Schr"odinger Bridge framework for peptide sequence design that maintains high-likelihood sequences and incorporates guidance towards functional objectives, improving peptide generation efficiency.

Contribution

MadSBM is the first discrete Schr"odinger Bridge model for peptide design that uses a biologically informed reference process and controlled transition rates for efficient, high-likelihood sequence generation.

Findings

Successfully generates peptide sequences near high-likelihood regions.

Incorporates functional guidance to expand therapeutic peptide design.

First application of discrete classifier guidance in Schr"odinger bridge models.

Abstract

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 Schr\"odinger 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 Schr\"odinger bridge-based generative models.