Diffusion MRI is highly influenced by diffusion boundaries created by microscopic cells and blood-filled vessels. The Gaussian phase approximation is a common method to analyze the signal evolution in the presence of diffusion. However, the Gaussian phase approximation exhibits several drawbacks as it is only valid for strong diffusion effects, it does not provide phase information and it yields only the total magnetization. In this work, we generalize the traditional Gaussian phase approximation and solve the mentioned issues. The new Gaussian local phase approximation is then applied to diffusion restricted between two slabs, within a cylinder and within a sphere.