This paper focuses on the correspondence field estimation and utilizes the estimation performance to compress stereoscopic images. This paper proposes the dense correspondence estimation with new probabilistic diffusion algorithm based on maximum a posteriori (MAP) estimation. The MAP-based correspondence field estimation including occlusion and line field is derived with reflecting the probabilistic distribution of the neighborhoods, and is applied to the compression of stereoscopic images. The proposed probabilistic diffusion algorithm considers the neighborhoods in Markov random field (MRF) with their joint probability density, which is the main difference from the previous MAP-based algorithms. The joint probability density of neighborhood system is implemented by using the probabilistic plane configuration model. And, the paper derives the upper and lower bounds of the probabilistic diffusion to analyze the stability of the iterative diffusion. In stereoscopic images compression, the proposed correspondence estimation is applied to quadtree-decomposed blocks. The probabilistic diffusion is modified in the multiresolution structure since the configurations of the neighborhood are different from those of uniform blocks or pixels. According to the experiments, the proposed algorithm had good estimation performance with fast convergence. Especially, the dense correspondence map was improved at the object boundary by combination of correspondence and line field in the probabilistic diffusion. Furthermore, the compression performance was improved by the disparity-compensated coding in the multiresolution structure.