© 2016 SPIE. X-ray diffraction tomography (XRDT) is a well-established technique that makes it possible to identify the material composition of an object throughout its volume. We show that using coded apertures to structure the measured scatter signal gives rise to a family of imaging architectures than enables snapshot XRDT in up to 4-dimensions. We consider pencil, fan, and cone beam snapshot XRDT and show results from both experimental and simulation-based studies. We find that, while lower-dimensional systems typically result in higher imaging fidelity, higher-dimensional systems can perform adequately for a specific task at orders of magnitude faster scan times.