Diffractive optical elements (DOEs) are promising in computational imaging because they can drastically reduce the size and weight of imaging devices compared to their refractive counterparts. However, the inherent strong dispersion limits their use in full spectrum imaging, causing unacceptable loss of color fidelity. In particular, metamerism introduces a data dependency in the image blur, which has been neglected in computational imaging methods. We introduce both a diffractive achromat based on computational optimization, as well as a corresponding cross-scale algorithm for correction of residual aberrations. The height profile of a diffractive lens is optimized to balance the focusing contributions of different wavelengths. The nearly identical spectral point spread functions (PSFs) create approximately spectrally invariant blur kernels. This property guarantees good color preservation and facilitates correction of residual aberrations in our fast two-step deconvolution without additional color priors. We demonstrate a diffractive achromat on a 0.5mm ultrathin substrate, with producing high color fidelity and better image quality in full visible spectrum.