Designing binders to target undruggable proteins presents a formidable challenge in drug discovery, requiring innovative approaches to overcome the lack of putative binding sites. Recently, generative models have been trained to design binding proteins via three-dimensional structures of target proteins, but as a result, struggle to design binders to disordered or conformationally unstable targets. In this work, we provide a generalizable algorithmic framework to design short, target-binding linear peptides, requiring only the amino acid sequence of the target protein. To do this, we propose a process to generate naturalistic peptide candidates through Gaussian perturbation of the peptidic latent space of the ESM-2 protein language model, and subsequently screen these novel linear sequences for target-selective interaction activity via a CLIP-based contrastive learning architecture. By integrating these generative and discriminative steps, we create a