The goal of this paper is to correct bleed-through in degraded documents using a variational approach. The variational model is adapted using an estimated background according to the availability of the verso side of the document image. Furthermore, for the latter case, a more advanced model based on a global control, the flow field, is introduced. The solution of each resulting model is obtained using wavelet shrinkage or a time-stepping scheme, depending on the complexity and nonlinearity of the models. When both sides of the document are available, the proposed model uses the reverse diffusion process for the enhancement of double-sided document images. The results of experiments with real and synthesized samples are promising. The proposed model, which is robust with respect to noise and complex background, can also be applied to other fields of image processing.