Ship design is a years-long process that requires balancing complex design trade-offs to create a ship that is efficient and effective. Finding new ways to improve the ship design process can lead to significant cost savings for ship building and operation. One promising technology is generative artificial intelligence, which has been shown to reduce design cycle time and create novel, high-performing designs. In literature review, generative artificial intelligence has been shown to generate ship hulls; however, ship design is particularly difficult as the hull of a ship requires the consideration of many objectives. This paper presents a study on the generation of parametric ship hull designs using a parametric diffusion model that considers multiple objectives and constraints for the hulls. This denoising diffusion probabilistic model (DDPM) generates the tabular parametric design vectors of a ship hull for evaluation. In addition to a tabular DDPM, this paper details adding guidance to improve the quality of generated ship hull designs. By leveraging classifier guidance, the DDPM produced feasible parametric ship hulls that maintain the coverage of the initial training dataset of ship hulls with a 99.5% rate, a 149x improvement over random sampling of the design vector parameters across the design space. Parametric ship hulls produced with performance guidance saw an average of 91.4% reduction in wave drag coefficients and an average of a 47.9x relative increase in the total displaced volume of the hulls compared to the mean performance of the hulls in the training dataset. The use of a DDPM to generate parametric ship hulls can reduce design time by generating high-performing hull designs for future analysis. These generated hulls have low drag and high volume, which can reduce the cost of operating a ship and increase its potential to generate revenue.