Hybrid Diffusion–Schrödinger Dynamics with Unified Learning for Target-Conditioned Peptide Co-Design

Target-conditioned peptide co-design is inherently challenging, as the generated peptides must exhibit biologically plausible sequences and structurally valid conformations. This difficulty is further amplified by the strong constraints imposed by the target protein, requiring physicochemical compatibility and geometric complementarity with the binding interface. Under these coupled constraints, existing methods often struggle to generate bindable peptides, resulting in limited binding success rates. In this paper, we propose PepHyD, a hybrid generative dynamics framework that formulates peptide co-design as a transition from broad sequence–structure exploration to target-directed transport. Specifically, PepHyD adapts the generative dynamics to the evolving state of generation, transitioning from diffusion-driven exploration of diverse peptide configurations to Schr\"odinger bridge transport that progressively concentrates intermediate representations toward target-compatible states. This design accommodates early-stage uncertainty while progressively enforcing target-specific constraints. Moreover, we introduce a unified target parameterization for both dynamics, allowing them to be learned within a shared denoising framework. Extensive experiments on LNR and BioDB demonstrate state-of-the-art performance, while evaluations on unseen targets and binding pockets further show strong generalization.