Non-destructive evaluation of plastically deformed metals is particularly valuable both for assessing dislocation microstructures and validating constitutive models. Among other methods, diffraction line profile analysis has been widely used to extract dislocation densities in deformed bulk single crystals and polycrystals. To date, the interpretation of whole line diffraction profiles relies on the use of semi-analytical models such as the extended convolutional multiple whole profile (eCMWP) method. This study proposes and assesses the prospects of a data-driven approach to extract dislocation densities from experimentally gathered whole line diffraction profiles. A database of virtual diffraction whole line profiles of Ta single crystals containing varying dislocation densities is generated. The dislocation microstructures are synthesized using discrete dislocation dynamics, and two distinct strain-based virtual diffraction algorithms are used to generate diffraction profiles. Instrumental broadening is applied to the synthetic profiles. The databases inform two Gaussian process regression-based surrogate models, allowing dislocation densities to be extracted from experimental profiles. The method is applied to 11 experimentally obtained whole line diffraction profiles gathered from plastically deformed Ta polycrystals. Upon applying both surrogate models to the experimental data and using eCMWP as a point of comparison, it is found that data-driven predictions of dislocation density can clearly capture the evolution of dislocation density with applied strain. Finally, the data-driven model is used to explore the effect of heterogeneous dislocation densities in microstructures containing grains, which may lead to more accurate data-driven predictions of dislocation density in plastically deformed polycrystals.