In this talk, I will present a new stable model of classical linear logic based on groupoids and profunctors between them. It can be seen as a refinement of the model of generalized species of structures introduced by Fiore et al. This refinement is based on an orthogonality on subgroups of endomorphisms for each object in a groupoid and it can also be translated to an orthogonality on the category of presheaves associated with a groupoid. The resulting bicategory is a model of differential linear logic where the functors in the cartesian closed Kleisli bicategory are precisely those satisfying a stability condition as studied by Berry, Girard, Taylor and many others. This is joint work with Marcelo Fiore and Hugo Paquet.