Understanding atomic hydrogen (H) diffusion in multi-principal element alloys (MPEAs) is crucial for enhancing hydrogen transport and storage technologies. However, the vast compositional space and complex chemical environments of MPEAs pose significant challenges. We develop highly accurate machine learning potentials and neural network-driven kinetic Monte Carlo simulations to investigate H diffusion in body-centered cubic (BCC) MoNbTaW MPEAs. H diffusion exhibits super-Arrhenius behavior in MPEAs, controlled by the low percentile of the H solution energy spectrum. Robust analytical models are derived via machine learning symbolic regression to predict H diffusivity across general BCC MPEAs. Additionally, chemical short-range order (SRO) generally does not impact H diffusion, except it enhances diffusion when H-favoring elements are present in low concentrations. These insights not only deepen our understanding of H diffusion dynamics in MPEAs but also guide the strategic development of advanced MPEAs for hydrogen-related applications by manipulating element type, composition, and SRO.