Background phase errors in 4D Flow MRI may negatively impact blood flow quantification. In this study, we assessed their impact on cerebrovascular flow volume measurements, evaluated the benefit of manual image-based correction, and assessed the potential of a convolutional neural network (CNN), a form of deep learning, to directly infer the correction vector field. With IRB waiver of informed consent, we retrospectively identified 96 MRI exams from 48 patients who underwent cerebrovascular 4D Flow MRI from October 2015 to 2020. Flow measurements of the anterior, posterior, and venous circulation were performed to assess inflow-outflow error and the benefit of manual image-based phase error correction. A CNN was then trained to directly infer the phase-error correction field, without segmentation, from 4D Flow volumes to automate correction, reserving from 23 exams for testing. Statistical analyses included Spearman correlation, Bland–Altman, Wilcoxon-signed rank (WSR) and F-tests. Prior to correction, there was strong correlation between inflow and outflow (ρ= 0.833–0.947) measurements with the largest discrepancy in the venous circulation. Manual phase error correction improved inflow-outflow correlation (ρ= 0.945–0.981) and decreased variance (p< 0.001,F-test). Fully automated CNN correction was non-inferior to manual correction with no significant differences in correlation (ρ= 0.971 vsρ= 0.982) or bias (p= 0.82,Wilcoxon-Signed Rank test) of inflow and outflow measurements. Residual background phase error can impair inflow-outflow consistency of cerebrovascular flow volume measurements. A CNN can be used to directly infer the phase-error vector field to fully automate phase error correction.