Shallow-depth whole-genome sequencing (WGS) of circulating cell-free DNA (ccfDNA) is a popular approach for non-invasive genomic screening assays, including liquid biopsy for early detection of invasive tumors as well as non-invasive prenatal screening (NIPS) for common fetal trisomies. In contrast to nuclear DNA WGS, ccfDNA WGS exhibits extensive inter- and intra- sample coverage variability that is not fully explained by typical sources of variation in WGS, such as GC content. This variability may inflate false positive and false negative screening rates of copy-number alterations and aneuploidy, particularly if these features are present at a relatively low proportion of total sequenced content. Herein, we propose an empirically-driven coverage correction strategy that leverages prior annotation information in a multi-distance learning context to improve within-sample coverage profile correction. Specifically, we train a weighted k-nearest neighbors-style method on non-pregnant female donor ccfDNA WGS samples, and apply it to NIPS samples to evaluate coverage profile variability reduction. We additionally characterize improvement in the discrimination of positive fetal trisomy cases relative to normal controls, and compare our results against a more traditional regression-based approach to profile coverage correction based on GC content and mappability. Under cross-validation, performance measures indicated benefit to combining the two feature sets relative to either in isolation. We also observed substantial improvement in coverage profile variability reduction in leave-out clinical NIPS samples, with variability reduced by 26.5-53.5% relative to the standard regression-based method as quantified by median absolute deviation. Finally, we observed improvement discrimination for screening positive trisomy cases reducing ccfDNA WGS coverage variability while additionally improving NIPS trisomy screening assay performance. Overall, our results indicate that machine learning approaches can substantially improve ccfDNA WGS coverage profile correction and downstream analyses.