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

2026-01-29

AI Summary

Peptide sequence generation faces significant challenges in discrete, highly constrained spaces, where sampling often becomes trapped in low-likelihood regions and suffers from inefficiency. This work proposes modeling the generation process as a controlled continuous-time Markov process over an amino acid editing graph. It introduces, for the first time, discrete classifier guidance within the Schrödinger bridge framework and leverages logits from pretrained protein language models to construct a biologically informed reference process. By learning a time-dependent control field, the method steers the generative trajectory toward high-likelihood regions, substantially reducing the number of sampling steps and avoiding nonviable intermediate states. This approach not only enhances chemical plausibility but also effectively expands the functional design space for therapeutic peptides.

Technology Category

• Natural Language Processing: Generation
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• peptide sequence design
• discrete generative modeling
• chemically implausible intermediates
• low-likelihood regions
• sampling efficiency

Innovation

• Schrödinger bridge
• discrete generative modeling
• peptide design
• continuous-time Markov process
• classifier guidance