Diffusion in combination with measurement noise erase high-frequency water isotope variability in ice cores, linking measurement precision to recoverable resolution. We derive expressions for this relationship, finding a resolution improvement of 1.5 times for a 10-fold measurement noise reduction. Based on the current age-depth model, our method predicts 10 000-year cycles will be recoverable in the 1.5 Myr old ice from the Oldest Ice Core δ¹⁸O record if a noise level of 0.01 ‰ is achieved.