Abstract: In scanning microscopy, drift causes the specimen to be sampled at positions displaced from the nominal probe positions. This displacement alters the spatial assignment of the recorded signals and biases quantitative measurements across two-dimensional imaging, channel-resolved spectroscopic mapping, and scan-position-resolved diffraction analysis. Here, we extend orthogonal-scan drift correction from 2D images to spectrum images and diffraction datasets. We demonstrate how to recover probe positions using either differently oriented multidimensional scans or structural reference images. The recovered positions are used either to resample the multidimensional data onto a regular grid or to assign each recorded signal to its corrected coordinate. Our method combines affine and non-rigid correction, requires no prior structural model, and is implemented as open-source, GPU-accelerated software that reduces processing times by two to three orders of magnitude, enabling routine and automated drift correction for quantitative multidimensional microscopy.