Implicit Diffusion: Efficient Optimization through Stochastic Sampling
Authors: name: Pierre Marion, name: Anna Korba, name: Peter Bartlett, name: Mathieu Blondel, name: Valentin De Bortoli, name: Arnaud Doucet, name: Felipe Llinares-López, name: Courtney Paquette, name: Quentin Berthet

We present a new algorithm to optimize distributions defined implicitly by
parameterized stochastic diffusions. Doing so allows us to modify the outcome
distribution of sampling processes by optimizing over their parameters. We
introduce a general framework for first-order optimization of these processes,
that performs jointly, in a single loop, optimization and sampling steps. This
approach is inspired by recent advances in bilevel optimization and automatic
implicit differentiation, leveraging the point of view of sampling as
optimization over the space of probability distributions. We provide
theoretical guarantees on the performance of our method, as well as
experimental results demonstrating its effectiveness in real-world settings.