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We propose a versatile deep image compression network based on Spatial Feature Transform (SFT) [47], which takes a source image and a corresponding quality map as inputs and produce a compressed image with variable rates. Our model covers a wide range of compression rates using a single model, which is controlled by arbitrary pixel-wise quality maps. In addition, the proposed framework allows us to perform task-aware image compressions for various tasks, e.g., classification, by efficiently estimating optimized quality maps specific to target tasks for our encoding network. This is even possible with a pretrained network without learning separate models for individual tasks. Our algorithm achieves outstanding rate-distortion trade-off compared to the approaches based on multiple models that are optimized separately for several different target rates. At the same level of compression, the proposed approach successfully improves performance on image classification and text region quality preservation via task-aware quality map estimation without additional model training. The code is available at the project website 1 .