We consider the problem of reconstructing the diffusion and absorption coefficients of the diffusion equation from internal information of the solution. In practice, the internal information is obtained from the first step of the inverse photoacoustic tomography, and is only partially provided near the boundary due to the high absorption property of the medium and the limitation of the equipment. Our main contribution is to prove a Hölder stability of the inverse problem in a subregion where the internal information is reliably supplied based on the stability estimation of a Cauchy problem satisfied by the diffusion coefficient. The exponent of the Hölder stability converges to a positive constant independent of the subregion as the subregion contracts towards the boundary. Numerical experiments demonstrates that it is possible to locally reconstruct the diffusion and absorption coefficients for smooth and even discontinuous media.