Differential Inference is the use of differentiation to perform probabilistic inference. The technique itself is relatively straightforward and plays nicely with autodiff: it roughly just automates Bayes' rule the way autodiff automates the chain rule. However, there is still a tendency for students to get tied up in the knots of even elementary probabilistic inference. Inspired by polemics that shined light on autodifferentiation, this talk will be half a tutorial on the use of differential inference and half a demonstration of all the fun math that it can remove from your life.