Abstract: Although image super-resolution (SR) problem has experienced unprecedented restoration accuracy with deep neural networks, it has yet limited versatile applications due to the substantial computational costs. Since different input images for SR face different restoration difficulties, adapting computational costs based on the input image, referred to as adaptive inference, has emerged as a promising solution to compress SR networks. Specifically, adapting the quantization bit-widths has successfully reduced the inference and memory cost without sacrificing the accuracy. However, despite the benefits of the resultant adaptive network, existing works rely on time-intensive quantization-aware training with full access to the original training pairs to learn the appropriate bit allocation policies, which limits its ubiquitous usage. To this end, we introduce the first on-the-fly adaptive quantization framework that accelerates the processing time from hours to seconds. We formulate the bit allocation problem with only two bit mapping modules: one to map the input image to the image-wise bit adaptation factor and one to obtain the layer-wise adaptation factors. These bit mappings are calibrated and fine-tuned using only a small number of calibration images. We achieve competitive performance with the previous adaptive quantization methods, while the processing time is accelerated by $\times$2000. Codes are available at https://github.com/Cheeun/AdaBM.