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Tracking the dynamics of fluorescent nanoparticles during embryonic development allows insights into the physical state of the embryo and, potentially, molecular processes governing developmental mechanisms. In this work, we investigate the motion of individual fluorescent nanodiamonds micro-injected into Drosophila melanogaster embryos prior to cellularisation. Fluorescence correlation spectroscopy and wide-field imaging techniques are applied to individual fluorescent nanodiamonds in blastoderm cells during stage 5 of development to a depth of ~40 \mu m. The majority of nanodiamonds in the blastoderm cells during cellularisation exhibit free diffusion with an average diffusion coefficient of (6 $\pm$ 3) x 10$^{-3}$ \mu m$^2$/s, (mean $\pm$ SD). Driven motion in the blastoderm cells was also observed with an average velocity of 0.13 $\pm$ 0.10 \mu m/s (mean $\pm$ SD) \mu m/s and an average applied force of 0.07 $\pm$ 0.05 pN (mean $\pm$ SD). Nanodiamonds in the periplasm between the nuclei and yolk were also found to undergo free diffusion with a significantly larger diffusion coefficient of (63 $\pm$ 35) x10$^{-3}$ \mu m$^2$/s (mean $\pm$ SD). Driven motion in this region exhibited similar average velocities and applied forces compared to the blastoderm cells indicating the transport dynamics in the two cytoplasmic regions are analogous.