This paper addresses image rescaling, the task of which is to downscale an input image followed by upscaling for the purposes of transmission, storage, or playback on heterogeneous devices. The state-of-the-art image rescaling network (known as IRN) tackles image downscaling and upscaling as mutually invertible tasks using invertible affine coupling layers. In particular, for upscaling, IRN models the missing high-frequency component by an input-independent (case-agnostic) Gaussian noise. In this work, we take one step further to predict a case-specific high-frequency component from textures embedded in the downscaled image. Moreover, we adopt integer coupling layers to avoid quantizing the downscaled image. When tested on commonly used datasets, the proposed method, termed DIRECT, improves high-resolution reconstruction quality both subjectively and objectively, while maintaining visually pleasing downscaled images.