Stability of the spatially homogeneous Landau equation in relative entropy and applications to score-based numerical methods

We give a short and elementary proof of stability for strong solutions of the spatially homogeneous Landau equation with Coulomb collisions, measured in relative entropy. The argument yields an explicit differential inequality for relative entropy under natural moment and regularity assumptions. The same computation provides an a posteriori error bound for score-based transport modeling and related deterministic numerical schemes, linking the training loss to the relative-entropy error.