Recent advances in generative models for medical imaging have shown promise in representing multiple modalities. However, the variability in modality availability across datasets limits the general applicability of the synthetic data they produce. To address this, we present a novel physics-informed generative model capable of synthesizing a variable number of brain MRI modalities, including those not present in the original dataset. Our approach utilizes latent diffusion models and a two-step generative process: first, unobserved physical tissue property maps are synthesized using a latent diffusion model, and then these maps are combined with a physical signal model to generate the final MRI scan. Our experiments demonstrate the efficacy of this approach in generating unseen MR contrasts and preserving physical plausibility. Furthermore, we validate the distributions of generated tissue properties by comparing them to those measured in real brain tissue.