U-Net has become a cornerstone in various visual applications such as image segmentation and diffusion probability models. While numerous innovative designs and improvements have been introduced by incorporating transformers or MLPs, the networks are still limited to linearly modeling patterns as well as the deficient interpretability. To address these challenges, our intuition is inspired by the impressive results of the Kolmogorov-Arnold Networks (KANs) in terms of accuracy and interpretability, which reshape the neural network learning via the stack of non-linear learnable activation functions derived from the Kolmogorov-Anold representation theorem. Specifically, in this paper, we explore the untapped potential of KANs in improving backbones for vision tasks. We investigate, modify and re-design the established U-Net pipeline by integrating the dedicated KAN layers on the tokenized intermediate representation, termed U-KAN. Rigorous medical image segmentation benchmarks verify the superiority of UKAN by higher accuracy even with less computation cost. We further delved into the potential of U-KAN as an alternative U-Net noise predictor in diffusion models, demonstrating its applicability in generating task-oriented model architectures.