Snapshot compressive imaging (SCI) is an advanced approach for single-shot high-dimensional data visualization. Deep learning is popularly used to improve SCI's performance. However, most existing methods are merely used as a replacement for analytical-modeling-based image reconstruction. Moreover, these models cling to the conventional random coded apertures and often presume a linear shearing operation. To overcome these limitations, we develop a new end-to-end convolutional neural network, termed deep high-dimensional adaptive net (D-HAN) that offers multi-faceted supervision to SCI by optimizing the coded aperture, sensing the shearing operation, and reconstructing three-dimensional datacubes. The D-HAN is implemented in two representative SCI systems for ultrahigh-speed imaging and hyperspectral imaging. The D-HAN is envisioned to benefit SCI in system design, image reconstruction, and performance evaluation.