The adoption of emerging imaging technologies in the medical community is often hampered if they provide a new unfamiliar contrast that requires experience to be interpreted. Here, in order to facilitate such integration, we developed two complementary machine learning approaches, respectively based on feature engineering and on convolutional neural networks (CNN), to perform automatic diagnosis of breast biopsies using dynamic full field optical coherence tomography (D-FF-OCT) microscopy. This new technique provides fast, high resolution images of biopsies with a contrast similar to H&E histology, but without any tissue preparation and alteration. We conducted a pilot study on 51 breast biopsies, and more than 1,000 individual images, and performed standard histology to obtain each biopsy diagnosis. Using our automatic diagnosis algorithms, we obtained an accuracy above 88% at the image level, and above 96% at the biopsy level. Finally, we proposed different strategies to narrow down the spatial scale of the automatic segmentation in order to be able to draw the tumor margins by drawing attention maps with the CNN approach, or by performing high resolution precise annotation of the datasets. Altogether, these results demonstrate the high potential of D-FF-OCT coupled to machine learning to provide a rapid, automatic, and accurate histopathology diagnosis.