Multi-dimensional optical imaging systems that simultaneously gather intensity, depth, polarimetric, and spectral information have numerous applications in medical sciences, robotics, and surveillance. Nevertheless, most current approaches require mechanical moving parts or multiple modulation processes and thus suffer from long acquisition time, high system complexity, or low sampling resolution. Here, a methodology to build snapshot multi-dimensional lensless imaging is proposed by combining planar-optics and computational technology, benefiting from sufficient flexibilities in optical engineering and robust information reconstructions. Specifically, a liquid crystal diffuser based on geometric phase modulation is designed to simultaneously encode the spatial, spectral, and polarization information of an object into a snapshot detected speckle pattern. At the same time, a post-processing algorithm acts as a special decoder to recover the hidden information in the speckle with the independent and unique point spread function related to the position, wavelength, and chirality. With the merits of snapshot acquisition, multi-dimensional perception ability, simple optical configuration, and compact device size, our approach can find broad potential applications in object recognition and classification.