Denoising Diffusion Probabilistic Models (DDPMs) have emerged as a potent class of generative models, demonstrating exemplary performance across diverse artificial intelligence domains such as computer vision and natural language processing. In the realm of protein design, while there have been advances in structure-based, graph-based, and discrete sequence-based diffusion, the exploration of continuous latent space diffusion within protein language models (pLMs) remains nascent. In this work, we introduce AMP-Diffusion, a latent space diffusion model tailored for antimicrobial peptide (AMP) design, harnessing the capabilities of the state-of-the-art pLM, ESM-2, to de novo generate functional AMPs for downstream experimental application. Our evaluations reveal that peptides generated by AMP-Diffusion align closely in both pseudo-perplexity and amino acid diversity when benchmarked against experimentally-validated AMPs, and further exhibit relevant physicochemical properties of naturally-occurring AMPs. Overall, these findings underscore the biological plausibility of our generated sequences and pave the way for their empirical validation. In total, our framework motivates future exploration of pLM-based diffusion models for peptide and protein design.