Diffusion MRI (dMRI) of the developing brain can provide valuable insights into the white matter development. However, slice thickness in fetal dMRI is typically high (i.e., 3-5 mm) to freeze the in-plane motion, which reduces the sensitivity of the dMRI signal to the underlying anatomy. In this study, we aim at overcoming this problem by using autoencoders to learn unsupervised efficient representations of brain slices in a latent space, using raw dMRI signals and their spherical harmonics (SH) representation. We first learn and quantitatively validate the autoencoders on the developing Human Connectome Project pre-term newborn data, and further test the method on fetal data. Our results show that the autoencoder in the signal domain better synthesized the raw signal. Interestingly, the fractional anisotropy and, to a lesser extent, the mean diffusivity, are best recovered in missing slices by using the autoencoder trained with SH coefficients. A comparison was performed with the same maps reconstructed using an autoencoder trained with raw signals, as well as conventional interpolation methods of raw signals and SH coefficients. From these results, we conclude that the recovery of missing/corrupted slices should be performed in the signal domain if the raw signal is aimed to be recovered, and in the SH domain if diffusion tensor properties (i.e., fractional anisotropy) are targeted. Notably, the trained autoencoders were able to generalize to fetal dMRI data acquired using a much smaller number of diffusion gradients and a lower b-value, where we qualitatively show the consistency of the estimated diffusion tensor maps.