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Abstract Background This study investigated the spatial relationship of 2-deoxy-2-[18F]-fluoro-D-glucose positron emission tomography ([18F]FDG-PET) standardized uptake values (SUVs) and apparent diffusion coefficients (ADCs) derived from magnetic resonance (MR) diffusion imaging on a voxel level using simultaneously acquired PET/MR data. We performed an institutional retrospective analysis of patients with newly diagnosed cervical cancer who received a pre-treatment simultaneously acquired [18F]FDG-PET/MR. Voxel SUV and ADC values, and global tumor metrics including maximum SUV (SUVmax), mean ADC (ADCmean), and mean tumor-to-muscle ADC ratio (ADCT/M) were compared. The impacts of histology, grade, and tumor volume on the voxel SUV to ADC relationship were also evaluated. The potential prognostic value of the voxel SUV/ADC relationship was evaluated in an exploratory analysis using Kaplan-Meier/log-rank and univariate Cox analysis. Results Seventeen patients with PET/MR scans were identified. There was a significant inverse correlation between SUVmax and ADCmean, and SUVmax and ADCT/M. In the voxelwise analysis, squamous cell carcinomas (SCCAs) and poorly differentiated tumors showed a consistent significant inverse correlation between voxel SUV and ADC values; adenocarcinomas (AdenoCAs) and well/moderately differentiated tumors did not. The strength of the voxel SUV/ADC correlation varied with metabolic tumor volume (MTV). On log-rank analysis, the correlation between voxel SUV/ADC values was prognostic of disease-free survival (DFS). Conclusions In this hypothesis-generating study, a consistent inverse correlation between voxel SUV and ADC values was seen in SCCAs and poorly differentiated tumors. On univariate statistical analysis, correlation between voxel SUV and ADC values was prognostic for DFS.