Background and objective: Brain activity in premature newborns has traditionally been studied using electroencephalography (EEG), leading to substantial advances in our understanding of early neural development. However, since brain development takes root at the fetal stage, a critical window of this process remains largely unknown. The only technique capable of recording neural activity in the intrauterine environment is fetal magnetoencephalography (fMEG), but this approach presents challenges in terms of data quality and scarcity. Using artificial intelligence, the present research aims to transfer the well-established knowledge from EEG studies to fMEG to improve understanding of prenatal brain development, laying the foundations for better detection and treatment of potential pathologies. Methods: We developed an unpaired diffusion translation method based on dual diffusion bridges, which notably includes numerical integration improvements to obtain more qualitative results at a lower computational cost. Models were trained on our unpaired dataset of bursts of spontaneous activity from 30 high-resolution premature newborns EEG recordings and 44 fMEG recordings. Results: We demonstrate that our method achieves significant improvement upon previous results obtained with Generative Adversarial Networks (GANs), by almost 5% on the mean squared error in the time domain, and completely eliminating the mode collapse problem in the frequency domain, thus achieving near-perfect signal fidelity. Conclusion: We set a new state of the art in the EEG-fMEG unpaired translation problem, as our developed tool completely paves the way for early brain activity analysis. Overall, we also believe that our method could be reused for other unpaired signal translation applications.