The paper introduces a simple method for unsupervised domain adaptation (UDA) in semantic segmentation, which reduces the discrepancy between source and target distributions by swapping the low-frequency spectrum of images. The method, called Fourier Domain Adaptation (FDA), does not require any training beyond the primary task of semantic segmentation and uses a Fast Fourier Transform (FFT) and its inverse. The authors demonstrate that FDA can achieve state-of-the-art performance in benchmarks when integrated into a standard semantic segmentation model, outperforming more complex adversarial learning methods. The effectiveness of FDA is attributed to its ability to discount nuisance variability in the data, such as low-level statistics that do not affect the perception of high-level semantics. The paper also discusses the choice of the spectral neighborhood size and the use of multi-band transfer for improved performance. Experimental results on synthetic-to-real domain adaptation tasks show that FDA outperforms existing methods, including those that use adversarial training. The authors conclude that their simple method provides a robust and effective approach to UDA, suggesting that more sophisticated models may struggle to manage low-level nuisance variability.The paper introduces a simple method for unsupervised domain adaptation (UDA) in semantic segmentation, which reduces the discrepancy between source and target distributions by swapping the low-frequency spectrum of images. The method, called Fourier Domain Adaptation (FDA), does not require any training beyond the primary task of semantic segmentation and uses a Fast Fourier Transform (FFT) and its inverse. The authors demonstrate that FDA can achieve state-of-the-art performance in benchmarks when integrated into a standard semantic segmentation model, outperforming more complex adversarial learning methods. The effectiveness of FDA is attributed to its ability to discount nuisance variability in the data, such as low-level statistics that do not affect the perception of high-level semantics. The paper also discusses the choice of the spectral neighborhood size and the use of multi-band transfer for improved performance. Experimental results on synthetic-to-real domain adaptation tasks show that FDA outperforms existing methods, including those that use adversarial training. The authors conclude that their simple method provides a robust and effective approach to UDA, suggesting that more sophisticated models may struggle to manage low-level nuisance variability.