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We develop a novel strategy to generate synthetic tumors. Unlike existing works, the tumors generated by our strategy have two intriguing advantages: (1) realistic in shape and texture, which even medical professionals can confuse with real tumors; (2) effective for AI model training, which can perform liver tumor segmentation similarly to a model trained on real tumors - this result is unprecedented because no existing work, using synthetic tumors only, has thus far reached a similar or even close performance to the model trained on real tumors. This result also implies that manual efforts for developing per-voxel annotation of tumors (which took years to create) can be considerably reduced for training AI models in the future. Moreover, our synthetic tumors have the potential to improve the success rate of small tumor detection by automatically generating enormous examples of small (or tiny) synthetic tumors.