You are right in that the use-cases are very similar to regular autodiff, with the added benefit that the returned gradient also accounts for the effects of taking alternative branches.

Just to clarify: we do a kind of source-to-source transformation by transparently injecting some API-calls in the right places (e.g., before branching-statements) before compilation. However, the compiled program then returns the program output alongside the gradient.

For the continuous parts, the AD library that comes with DiscoGrad uses operator overloading.