We present a generative modeling framework for atomistic systems that combines score-based diffusion for atomic positions with a novel continuous-time discrete diffusion process for atomic types. This approach enables flexible and physically grounded generation of atomic structures across chemical and structural domains. Applied to metallic clusters and two-dimensional materials using the QCD and C2DB datasets, our models achieve strong performance in fidelity and diversity, evaluated using precision-recall metrics against synthetic baselines. We demonstrate atomic type interpolation for generating bimetallic clusters beyond the training distribution, and use classifier-free guidance to steer sampling toward specific crystallographic symmetries in two-dimensional materials. These capabilities are implemented in Atomistic Generative Diffusion (AGeDi), an open-source, extensible software package for atomistic generative diffusion modeling.