This paper introduces a novel cross-physiology translation task: synthesizing sleep electroencephalography (EEG) from respiration signals. To address the significant complexity gap between the two modalities, we propose a waveform-conditional generative framework that preserves fine-grained respiratory dynamics while constraining the EEG target space through discrete tokenization. Trained on over 28,000 individuals, our model achieves a 7% Mean Absolute Error in EEG spectrogram reconstruction. Beyond reconstruction, the synthesized EEG supports downstream tasks with performance comparable to ground truth EEG on age estimation (MAE 5.0 vs. 5.1 years), sex detection (AUROC 0.81 vs. 0.82), and sleep staging (Accuracy 0.84 vs. 0.88), significantly outperforming baselines trained directly on breathing. Finally, we demonstrate that the framework generalizes to contactless sensing by synthesizing EEG from wireless radio-frequency reflections, highlighting the feasibility of remote, non-contact neurological assessment during sleep.