It is a classical yet surprising result that noise can have a regularizing effect on differential equations. For example, adding a Brownian motion to an ODE with bounded and measurable vector field leads to a well posed equation with Lipschitz continuous flow, while the equation without noise may have none or many solutions. Classical proofs of this are based on stochastic analysis and on the link between Brownian motion and the heat equation. In that argument it is not obvious which property of the noise gives the regularization. A more recent approach by Catellier and Gubinelli leads to a pathwise understanding of regularization. I will present a simplified version of their approach and use it to construct "infinitely regularizing" paths: after adding them to an ODE we have a unique solution and an infinitely smooth flow - even if the vector field is only a tempered distribution. This is joint work with Fabian Harang.