Recently, CycleGAN was shown to provide high-performance, ultra-fast denoising for low-dose X-ray computed tomography (CT) without the need for a paired training dataset. Although this was possible thanks to cycle consistency, CycleGAN requires two generators and two discriminators to enforce cycle consistency, demanding significant GPU resources and technical skills for training. A recent proposal of switchable CycleGAN with Adaptive Instance Normalization (AdaIN) alleviates the problem in part by using a single generator. However, two discriminators and an additional AdaIN code generator are still required for training. To solve this problem, here we present a novel cycle-free CycleGAN architecture, which consists of a single generator and a discriminator but still guarantees the cycle consistency. The main innovation comes fromthe observation that the use of an invertible generator automatically fulfills the cycle consistency condition and eliminates the additional discriminator in the CycleGAN formulation. Extensive experiments using various levels of low-dose CT images confirm that our method can improve denoising performance using only 24% of learnable parameters, twice faster training time, and showed better trade-offs between the complexity versus reconstruction quality, compared to the existing methods.