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license: cc-by-nc-nd-4.0
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<h1 align="center">
Minimal-Action Discrete Schrödinger Bridge Matching<br>
for Peptide Sequence Design
</h1>
<div align="center">
<a href="https://shreygoel09.github.io/" target="_blank">Shrey Goel</a><sup>1</sup> <b>·</b> 
<a href="https://www.chatterjeelab.com/" target="_blank">Pranam Chatterjee</a><sup>2<sup>
<br>
<p style="font-size: 16px;">
<sup>1</sup> Duke University  
<sup>2</sup> University of Pennsylvania  
</div>
<div align="center">
<a href="https://arxiv.org/abs/2601.22408v1"><img src="https://img.shields.io/badge/Arxiv-2601.22408-red?style=for-the-badge&logo=Arxiv" alt="arXiv"/></a>
</div>
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 many 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 produce probability trajectories that remain within high-likelihood sequence neighborhoods throughout generation, MadSBM:
1. Defines generation relative to a biologically informed reference process derived from pretrained protein language model logits.
2. Learns a time-dependent control field that biases transition rates to induce low-action transport paths from a masked prior to the data distribution.
Finally, we introduce an objective-guided sampling procedure that steers MadSBM generation toward specific functional targets, representing—to our knowledge—the first application of discrete classifier guidance within a Schrödinger bridge-based generative framework.
## **Repository Authors**
- <u>[Shrey Goel](https://shreygoel09.github.io/)</u> – undergraduate student at Duke University
- <u>[Pranam Chatterjee](mailto:pranam@seas.upenn.edu)</u> – Assistant Professor at University of Pennsylvania
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