Understanding the effective diffusion coefficient (D) is crucial for describing atomic transport during crystal nucleation in supercooled liquids and glasses. However, pinpointing the key structural units driving crystallization in intricate, multicomponent glass-formers remains a challenge. This study presents a novel analysis of lithium diborate (Li₂O·2 B₂O₃ - LB₂) crystallization in supercooled and glassy states by using available viscosity and crystallization data for samples of the same batch. An original key feature is that the nucleation rates were measured using a single-stage rather than the traditional double-stage heat treatment. We compared three proxies for D: Dη obtained from viscosity, DU derived from crystal growth rates, and Dτ estimated from nucleation time-lags. Our analysis revealed that at deep supercoolings, below the glass transition temperature, DU and Dτ yield similar steady-state nucleation rate estimates, which significantly exceed those predicted by using Dη (the most frequently used diffusion proxy). This result suggests that the atomic jumps governing crystal nucleation may be comparable to those in crystal growth, but distinct from those associated with cooperative rearrangements controlling viscous flow. Additionally, the estimated kinetic spinodal temperature (Tks) is above the Kauzmann temperature Tk, implying that crystal nucleation precedes relaxation to the supercooled liquid state, circumventing the entropy paradox and corroborating recent MD simulations for other substances. These findings are valuable for refining theoretical models of crystal nucleation and highlight the complexities of the glassy state.