While supervised deep neural networks have become the dominant method for image analysis tasks in bioimages, truly versatile methods are not available yet because of the diversity of modalities and conditions and the cost of retraining. In practice, day-to-day biological image analysis still largely relies on ad hoc workflows often using classical linear filters. We propose NU-Net, a convolutional neural network filter selectively enhancing cells and nuclei, as a drop-in replacement of chains of classical linear filters in bioimage analysis pipelines. Using a style transfer architecture, a novel perceptual loss implicitly learns a soft separation of background and foreground. We used self-supervised training using 25 datasets covering diverse modalities of nuclear and cellular images. We show its ability to selectively improve contrast, remove background and enhance objects across a wide range of datasets and workflow while keeping image content. The pre-trained models are light and practical, and published as free and open-source software for the community. NU-Net is also available as a plugin for Napari.