  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 $^{83\mathrm{m}}$Kr calibration electron captures ($E\sim45$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$\geq$1.5MeV), yielding a precision of 3cm on the
event barycenter. The precision achieved with these methods indicates the
feasibility energy calibrations of better than 1% FWHM at Q$_{\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.
