title: Implicit Diffusion: Efficient Optimization through Stochastic Sampling
summary: 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.
paper_authors._id: 65c5a299b4fa1caf9655e53d
paper_authors.name: Pierre Marion
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paper_authors.fullname: Pierre Marion
paper_authors.type: user
paper_authors.user: PierreMarion
paper_authors._id: 65c5a299b4fa1caf9655e53e
paper_authors.name: Anna Korba
paper_authors._id: 65c5a299b4fa1caf9655e53f
paper_authors.name: Peter Bartlett
paper_authors._id: 65c5a299b4fa1caf9655e540
paper_authors.name: Mathieu Blondel
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paper_authors.fullname: Mathieu Blondel
paper_authors.type: user
paper_authors.user: mblondel
paper_authors._id: 65c5a299b4fa1caf9655e541
paper_authors.name: Valentin De Bortoli
paper_authors.status: admin_assigned
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paper_authors.fullname: Valentin De Bortoli
paper_authors.type: user
paper_authors.user: vdeborto
paper_authors._id: 65c5a299b4fa1caf9655e542
paper_authors.name: Arnaud Doucet
paper_authors._id: 65c5a299b4fa1caf9655e543
paper_authors.name: Felipe Llinares-López
paper_authors._id: 65c5a299b4fa1caf9655e544
paper_authors.name: Courtney Paquette
paper_authors._id: 65c5a299b4fa1caf9655e545
paper_authors.name: Quentin Berthet
paper_title: Implicit Diffusion: Efficient Optimization through Stochastic Sampling
paper_summary: 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.
paper_ai_summary: A novel algorithm optimizes implicit distributions defined by parameterized stochastic diffusions, enabling joint optimization and sampling in a single loop.
paper_ai_keywords: parameterized stochastic diffusions first-order optimization bilevel optimization automatic implicit differentiation