Minimal-Action Discrete Schrödinger Bridge Matching for Peptide Sequence Design

• URL: http://arxiv.org/abs/2601.22408v1
• Date: Thu, 29 Jan 2026 23:38:36 GMT
• Title: Minimal-Action Discrete Schrödinger Bridge Matching for Peptide Sequence Design
• Authors: Shrey Goel, Pranam Chatterjee,
• Abstract summary: We introduce Minimal-action discrete Schrdinger Bridge Matching (MadSBM) as a rate-based generative framework for peptide design.<n>MadSBM formulates generation as a controlled continuous-time Markov process on the amino-acid edit graph.<n>We introduce guidance to the MadSBM sampling procedure towards a specific functional objective, expanding the design space of therapeutic peptides.
• Score: 1.063850381314547
• License: http://creativecommons.org/licenses/by/4.0/
• 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 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.

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