This study presents a novel latent diffusion framework for generating clinically accurate virtual synthetic thrombi for use in in-silico clinical trials (ISCTs). The framework combines a variational autoencoder (VAE) with a diffusion model to generate three-dimensional representations of thrombi, including their shape, non-contrast computed tomography (NCCT) Hounsfield units, and computed tomography angiography (CTA) Hounsfield units. The model is trained on 1901 automatically segmented thrombi from the MR CLEAN registry. Additionally, we propose a method for incorporating thrombus composition characteristics into the virtual thrombi based on the relationship between NCCT imaging characteristics and red blood cell content, derived from in-vitro thrombus analogue histological analysis. The generated synthetic thrombi demonstrate clinically plausible characteristics across multiple dimensions, evaluated using key imaging metrics: thrombus attenuation increase (TAI) quartiles measuring perviousness, NCCT and CTA standard deviations quantifying heterogeneity, and median NCCT values indicating thrombus density. The synthetic samples show comparable distributions to the training data for these metrics, as well as for volume and surface area, while maintaining physiologically plausible ranges. The uniqueness of the samples is confirmed by low Intersection over Union (IoU) values between synthetic and real thrombi. The estimated histological compositions of synthetic thrombi align well with those observed in retrieved patient thrombi, though limitations exist in representing very low red blood cell content thrombi. This framework provides a foundation for generating realistic virtual thrombi that can be used to enhance ISCTs, particularly in the development and testing of new treatment options for acute ischemic stroke. Future work should focus on establishing connections between synthetic thrombi and vessels, and further exploring the relationship between imaging characteristics and thrombus composition through controlled in-vitro experiments.