Recently, diffuse reflectors are being incorporated into solar cells, due to the advantage of no metallic absorption loss, higher reflectance, decent light scattering property by embedded TiO2 scatterers, and the ease of fabrication. Different methods have been employed to analyze diffuse reflectors, including Monte Carlo method, N-flux method, and a one-dimensional approximation based on semi-coherent optics, and the calculated reflectance is around 80% by these methods. In this work, rigorous wave optics solution is used, and it is shown that the reflectance for diffuse medium mirrors can actually be as high as >99% over a broad spectral range, provided the TiO2 scatterer geometry is properly optimized. The bandwidth of diffuse reflectors is un-achievable by other dielectric mirrors such as distributed Bragg reflectors or high index contrast grating mirror, using the same index contrast. Finally, it is promisingly found that even if the distribution of TiO2 is random, the wide-band reflection can still be achieved for the optimized TiO2 geometry. Initial experimental result is included in the supplementary material which shows the high feasibility of diffuse medium mirrors for solar cells.