Therapeutic molecules must selectively interact with a target protein while avoiding structurally or functionally similar off-targets. However, no existing generative strategy explicitly optimizes both target affinity and off-target avoidance. To address this, we introduce SOAPIA, a framework for the Siamese-guided generation of Off-target-Avoiding Protein Interactions with high target Affinity. SOAPIA generates de novo peptide binders by steering the generative process of a Diffusion Protein Language Model (DPLM) using a multi-objective Monte Carlo Tree Search (MCTS). Affinity is optimized via a pre-trained predictor, while specificity is enforced using a Siamese model trained with an adaptive Log-Sum-Exp Decoy Loss. This dual-guidance scheme enables Pareto-efficient exploration of discrete sequence space without gradient access. In benchmarks across 18 fusion oncoproteins, SOAPIA consistently identifies binders with strong affinity and high selectivity. In a targeted case study, SOAPIA generated a peptide that preferentially binds DHRSX::RPS4Y1 by engaging both the head and tail domains of the fusion while avoiding the wild-type counterparts. These results underscore SOAPIA’s promise for designing safe, specific biologics for fusion-driven cancers and other rare, currently untreatable diseases.