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**
- [Shrey Goel](https://shreygoel09.github.io/) – undergraduate student at Duke University
- [Pranam Chatterjee](mailto:pranam@seas.upenn.edu) – Assistant Professor at University of Pennsylvania
