Abstract: Noble element time projection chambers are a leading technology for rare event detection in physics, such as for dark matter and neutrinoless double beta decay searches. Time projection chambers typically assign event position in the drift direction using the relative timing of prompt scintillation and delayed charge collection signals, allowing for reconstruction of an absolute position in the drift direction. In this paper, alternate methods for assigning event drift distance via quantification of electron diffusion in a pure high pressure xenon gas time projection chamber are explored. Data from the NEXT-White detector demonstrate the ability to achieve good position assignment accuracy for both high- and low-energy events. Using point-like energy deposits from Kr-83m calibration electron captures (E similar to 45 keV), the position of origin of low-energy events is determined to 2 cm precision with bias <1 mm. A convolutional neural network approach is then used to quantify diffusion for longer tracks (E >= 1.5 MeV), from radiogenic electrons, yielding a precision of 3 cm on the event barycenter. The precision achieved with these methods indicates the feasibility energy calibrations of better than 1% FWHM at Q(beta beta) in pure xenon, as well as the potential for event fiducialization in large future detectors using an alternate method that does not rely on primary scintillation.