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We present Curve Distillation, CuDi, for efficient and controllable exposure adjustment without the requirement of paired or unpaired data during training. Our method inherits the zero-reference learning and curve-based framework from an effective low-light image enhancement method, Zero-DCE, with further speed up in its inference speed, reduction in its model size, and extension to controllable exposure adjustment. The improved inference speed and lightweight model are achieved through novel curve distillation that approximates the time-consuming iterative operation in the conventional curve-based framework by high-order curve's tangent line. The controllable exposure adjustment is made possible with a new self-supervised spatial exposure control loss that constrains the exposure levels of different spatial regions of the output to be close to the brightness distribution of an exposure map serving as an input condition. Different from most existing methods that can only correct either underexposed or overexposed photos, our approach corrects both underexposed and overexposed photos with a single model. Notably, our approach can additionally adjust the exposure levels of a photo globally or locally with the guidance of an input condition exposure map, which can be pre-defined or manually set in the inference stage. Through extensive experiments, we show that our method is appealing for its fast, robust, and flexible performance, outperforming state-of-the-art methods in real scenes. Project page: https://li-chongyi.github.io/CuDi_files/.