Tomographic diffractive microscopy is a recent imaging technique that reconstructs quantitatively the three-dimensional permittivity map of a sample with a resolution better than that of conventional wide-field microscopy. Its main drawbacks lie in the complexity of the setup and in the slowness of the image recording as both the amplitude and the phase of the field scattered by the sample need to be measured for hundreds of successive illumination angles. In this Letter, we show that, using a wavefront sensor, tomographic diffractive microscopy can be implemented easily on a conventional microscope. Moreover, the number of illuminations can be dramatically decreased if a constrained reconstruction algorithm is used to recover the sample map of permittivity.