We present a polarization-based approach to perform diffuse-specular separation from a single polarimetric image, acquired using a flexible, practical capture setup. Our key technical insight is that, unlike previous polarization-based separation methods that assume completely unpolarized diffuse reflectance, we use a more general polarimetric model that accounts for partially polarized diffuse reflections. We capture the scene with a polarimetric sensor and produce an initial analytical diffuse-specular separation that we further pass into a deep network trained to refine the separation. We demonstrate that our combination of analytical separation and deep network refinement produces state-of-the-art diffuse-specular separation, which enables image-based appearance editing of dynamic scenes and enhanced appearance estimation.