Realistic models of human anatomy have long been an enabling ingredient for many medical image analysis methods, as they enable controlled developments and evaluations. Recently, computational models of human anatomy have received considerable attention for their use in “in silico imaging trials”, where artificial intelligence (AI) algorithms are evaluated on purely synthetic data to assess their adequacy for deployment. Traditional methods for anatomical modeling use pre-defined cohorts that are modeled with great effort which inhibits scalability. More recent techniques consider statistical approaches, including generative AI, to synthesize anatomical models but these methods have focused on grid-based representations that limit the achievable spatial resolution. Here we present a generative approach for computational human phantom modeling, designed to capture anatomical variability and address the limitations of existing methods outlined above. We use signed distance functions (SDF) for modeling organ shapes and a pose encoder for learning their spatial distribution. SDFs implicitly encode organ surfaces, thus allowing for high-resolution modeling, and provide a scalable way for learning organ shapes directly from segmentations, i.e. without requiring additional manual interventions. Furthermore, the biological variability of organ shapes is encoded within embeddings optimized during model training. Once trained, sampling in the latent space allows for the generation of new and anatomically plausible phantoms that can be rasterized at arbitrary spatial resolution. We evaluated our model quantitatively in terms of its reconstruction performance and qualitatively in terms of the anatomical plausibility of generated phantoms. In the reconstruction task, our model achieved a mean absolute surface distance of under 2 mm and a Dice coefficient exceeding 85 % for most organs. We assessed the anatomical plausibility of our synthetic phantoms by using them to condition a generative diffusion model for producing realistic synthetic computed tomography images. Results demonstrate the scalability and versatility of the proposed approach for next-generation anatomical phantom modeling, with future work focusing on whole-body modeling.