Purpose: To characterize the voxel-wise uncertainties of Apparent Diffusion Coefficient (ADC) estimation from whole-body diffusion-weighted imaging (WBDWI). This enables the calculation of a new parametric map based on estimates of ADC and ADC uncertainty to improve WBDWI imaging standardization and interpretation: NoIse-Corrected Exponentially-weighted diffusion-weighted MRI (niceDWI). Methods: Three approaches to the joint modeling of voxel-wise ADC and ADC uncertainty (σ ADC) are evaluated: (i) direct weighted least squares (DWLS), (ii) iterative linear-weighted least-squares (IWLS), and (iii) smoothed IWLS (SIWLS). The statistical properties of these approaches in terms of ADC/σ ADC accuracy and precision is compared using Monte Carlo simulations. Our proposed post-processing methodology (niceDWI) is evaluated using an ice-water phantom, by comparing the contrast-to-noise ratio (CNR) with conventional exponentially-weighted DWI. We present the clinical feasibility of niceDWI in a pilot cohort of 16 patients with metastatic prostate cancer. Results: The statistical properties of ADC and σ ADC conformed closely to the theoretical predictions for DWLS, IWLS, and SIWLS fitting routines (a minor bias in parameter estimation is observed with DWLS). Ice-water phantom experiments demonstrated that a range of CNR could be generated using the niceDWI approach, and could improve CNR compared to conventional methods. We successfully implemented the niceDWI technique in our patient cohort, which visually improved the in-plane bias field compared with conventional WBDWI. Conclusions: Measurement of the statistical uncertainty in ADC estimation provides a practical way to standardize WBDWI across different scanners, by providing quantitative image signals that improve its reliability. Our proposed method can overcome inter-scanner and intra-scanner WBDWI signal variations that can confound image interpretation.