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Due to its specificity, fluorescence microscopy has become a quintessential imaging tool in cell biology. However, photobleaching, phototoxicity, and related artifacts continue to limit fluorescence microscopy’s utility. Recently, it has been shown that artificial intelligence (AI) can transform one form of contrast into another. We present phase imaging with computational specificity (PICS), a combination of quantitative phase imaging and AI, which provides information about unlabeled live cells with high specificity. Our imaging system allows for automatic training, while inference is built into the acquisition software and runs in real-time. Applying the computed fluorescence maps back to the quantitative phase imaging (QPI) data, we measured the growth of both nuclei and cytoplasm independently, over many days, without loss of viability. Using a QPI method that suppresses multiple scattering, we measured the dry …