In instance-level detection tasks (e.g., object detection), reducing input resolution is an easy option to improve runtime efficiency. However, this option traditionally hurts the detection performance much. This paper focuses on boosting the performance of low-resolution models by distilling knowledge from a high- or multi-resolution model. We first identify the challenge of applying knowledge distillation (KD) to teacher and student networks that act on different input resolutions. To tackle it, we explore the idea of spatially aligning feature maps between models of varying input resolutions by shifting feature pyramid positions and introduce aligned multi-scale training to train a multi-scale teacher that can distill its knowledge to a low-resolution student. Further, we propose crossing feature-level fusion to dynamically fuse teachers multi-resolution features to guide the student better. On several instance-level detection tasks and datasets, the low-resolution models trained via our approach perform competitively with high-resolution models trained via conventional multi-scale training, while outperforming the latters low-resolution models by 2.1% to 3.6% in terms of mAP. Our code is made publicly available at https://github.com/dvlab-research/MSAD.