The diffusion process is the basis of many branches of science and engineering, and generally obeys reciprocity between two ports of a linear time-invariant medium. Recent research on classical wave dynamics has explored the spatiotemporal modulation to exhibit preferred directions in photons and plasmons. Here we report a distinct rectification effect on diffusion-wave fields by modulating the conductivity and observe nonreciprocal transport of charges. We experimentally create a spatiotemporal diffusion metamaterial, in which a mode transition to zero frequency is realized. A direct current component thereby emerges, showcasing a biased effect on the charge diffusion when the incident fundamental frequency is a multiple of the system modulation frequency. These results may find applications spanning a plethora of diffusive fields in general.