The pursuit of high-quality remote sensing images never ceases. In the field of remote sensing image processing, addressing image denoising and deblurring is of paramount importance. To reconstruct original images from degraded ones, we propose adaptive fourth-order partial differential equation (PDE) models for denoising and denoising–deblurring based on a variational framework. The proposed PDE models include second-order, third-order, and fourth-order terms. The models fully utilize the advantages of second-order and third-order terms in preserving boundaries and the fourth-order term in denoising and avoiding the stair-step effect. By adaptively adjusting the coefficients of the second-order, third-order, and fourth-order terms during the denoising and denoising–deblurring processes, the models achieve a good balance between denoising and boundary preservation. In the homogeneous regions of the images, the fourth-order term dominates and performs well at removing noise, whereas in the edge regions, the slow diffusion of the second-order term and the reverse diffusion of the third-order term dominate, resulting in good boundary preservation. We discretize the models in time and space using the Rothe method and finite difference method, respectively. Numerical experiments demonstrate significant improvements over traditional methods. When the noise standard deviation is 20, the denoising model achieves an ∼2 dB increase in peak signal-to-noise ratio compared with the total variation method.