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The 3D Lookup Table (3D LUT) is a highly-efficient tool for real-time image enhancement tasks, which models a non-linear 3D color transform by sparsely sampling it into a discretized 3D lattice. Previous works have made efforts to learn image-adaptive output color values of LUTs for flexible enhancement but neglect the importance of sampling strategy. They adopt a sub-optimal uniform sampling point allocation, limiting the expressiveness of the learned LUTs since the (tri-)linear interpolation between uniform sampling points in the LUT transform might fail to model local non-linearities of the color transform. Focusing on this problem, we present AdaInt (Adaptive Intervals Learning), a novel mechanism to achieve a more flexible sampling point allocation by adaptively learning the non-uniform sampling intervals in the 3D color space. In this way, a 3D LUT can increase its capability by conducting dense sampling in color ranges requiring highly non-linear transforms and sparse sampling for near-linear transforms. The proposed AdaInt could be implemented as a compact and efficient plug-and-play module for a 3D LUT-based method. To enable the end-to-end learning of AdaInt, we design a novel differentiable operator called AiLUT-Transform (Adaptive Interval LUT Transform) to locate input colors in the non-uniform 3D LUT and provide gradients to the sampling intervals. Experiments demonstrate that methods equipped with AdaInt can achieve state-of-the-art performance on two public benchmark datasets with a negligible overhead increase. Our source code is available at https://github.com/ImCharlesY/AdaInt.