It is shown that regularizing the signal gradient statistics during training of deep-learning models of super-resolution fluorescence microscopy improves the generated images. Specifically, regularizing the images in the training data set is proposed to have gradient and Laplacian statistics closer to those expected for natural-scene images. The BioSR data set of matched pairs of diffraction-limited and super-resolution images is used to evaluate the proposed regularization in a state-of-the-art generative deep-learning model of super-resolution microscopy, the Conditional Variational Diffusion Model (CVDM). Since the proposed regularization is applied as a preprocessing step to the training data, it can be used in conjunction with any supervised machine-learning model. However, its utility is limited to images for which the prior is appropriate, which in the BioSR data set are the images of filamentous structures. The quality and generalization power of CVDM trained with and without the proposed regularization are compared, showing that the new prior yields images with clearer visual detail and better small-scale structure.