This paper proposes a hybrid machine learning framework for predicting the spatiotemporal progression of brain tumors. It combines a mathematical tumor growth model with a guided denoising diffusion implicit model (DDIM) to synthesize anatomically plausible future MRIs from previous scans. Formulated as a system of ordinary differential equations, the mechanical model captures temporal tumor dynamics, including the effects of radiation therapy, and estimates future tumor burden. These estimates condition the gradient-guided DDIM, enabling image synthesis that matches both predicted growth and patient anatomy. The model is trained on the BraTS adult and pediatric glioma dataset and evaluated on 60 axial slices from a case of pediatric diffuse midline glioma (DMG). The framework generates realistic follow-up scans based on a spatial similarity measure. Furthermore, it introduces a tumor growth probability map that captures both the extent and directionality of clinically relevant tumor growth, represented by the 95th percentile Hausdorff distance. This method enables biologically informed image generation in data-limited scenarios, providing generative spatiotemporal predictions that take mechanical prior information into account.
