Deep learning-based antimicrobial peptide (AMP) discovery faces critical challenges such as low experimental hit rates as well as the need for nuanced controllability and efficient modeling of peptide properties. To address these challenges, we introduce OmegAMP, a framework that leverages a diffusion-based generative model with efficient low-dimensional embeddings, precise controllability mechanisms, and novel classifiers with drastically reduced false positive rates for candidate filtering. OmegAMP enables the targeted generation of AMPs with specific physicochemical properties, activity profiles, and species-specific effectiveness. Moreover, it maximizes sample diversity while ensuring faithfulness to the underlying data distribution during generation. We demonstrate that OmegAMP achieves state-of-the-art performance across all stages of the AMP discovery pipeline, significantly advancing the potential of computational frameworks in combating antimicrobial resistance.