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We propose an asymmetrically cyclic adversarial network that performs denoising tasks to improve electron microscopy (EM) image analysis. Deep learning-based denoising methods have typically been trained either with matching pairs of noise-free and noise-corrupted images or by leveraging prior knowledge of noise distributions. Neither of these options is feasible in high-throughput EM imaging pipelines. Our proposed denoising method employs independently acquired noise-free, noise pattern, and noise-corrupted images to automatically learn the underlying noise model and generate denoised outputs. This method is based on three-way cyclic constraints with adversarial training of a deep network to improve the quality of acquired images without paired training data. Its utility is demonstrated for cases where imaging substrates add noise and where acquisition conditions contribute noise. We show that our method, which builds on the concept of CycleGAN, outperforms the current state-of-the-art denoising approaches Noise2Noise and Noise2Void, as well as other learning-based techniques.