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In Convolutional Neural Network (CNN) based image processing, most studies propose networks that are optimized to single-level (or single-objective); thus, they underperform on other levels and must be retrained for delivery of optimal performance. Using multiple models to cover multiple levels involves very high computational costs. To solve these problems, recent approaches train networks on two different levels and propose their own interpolation methods to enable arbitrary intermediate levels. However, many of them fail to generalize or have certain side effects in practical usage. In this paper, we define these frameworks as network tuning and interpolation and propose a novel module for continuous-level learning, called Filter Transition Network (FTN). This module is a structurally smoother module than existing ones. Therefore, the frameworks with FTN generalize well across various tasks and networks and cause fewer undesirable side effects. For stable learning of FTN, we additionally propose a method to initialize non-linear neural network layers with identity mappings. Extensive results for various image processing tasks indicate that the performance of FTN is comparable in multiple continuous levels, and is significantly smoother and lighter than that of other frameworks.