Implicit Diffusion: Efficient optimization through stochastic sampling

Pierre Marion, Anna Korba, Peter Bartlett, Mathieu Blondel, Valentin De Bortoli, Arnaud Doucet, Felipe Llinares-López, Courtney Paquette, Quentin Berthet
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:1999-2007, 2025.

Abstract

Sampling and automatic differentiation are both ubiquitous in modern machine learning. At its intersection, differentiating through a sampling operation, with respect to the parameters of the sampling process, is a problem that is both challenging and broadly applicable. We introduce a general framework and a new algorithm for first-order optimization of parameterized stochastic diffusions, performing 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 and experimental results showcasing the performance of our method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-marion25a, title = {Implicit Diffusion: Efficient optimization through stochastic sampling}, author = {Marion, Pierre and Korba, Anna and Bartlett, Peter and Blondel, Mathieu and Bortoli, Valentin De and Doucet, Arnaud and Llinares-L{\'o}pez, Felipe and Paquette, Courtney and Berthet, Quentin}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {1999--2007}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/marion25a/marion25a.pdf}, url = {https://proceedings.mlr.press/v258/marion25a.html}, abstract = {Sampling and automatic differentiation are both ubiquitous in modern machine learning. At its intersection, differentiating through a sampling operation, with respect to the parameters of the sampling process, is a problem that is both challenging and broadly applicable. We introduce a general framework and a new algorithm for first-order optimization of parameterized stochastic diffusions, performing 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 and experimental results showcasing the performance of our method.} }
Endnote
%0 Conference Paper %T Implicit Diffusion: Efficient optimization through stochastic sampling %A Pierre Marion %A Anna Korba %A Peter Bartlett %A Mathieu Blondel %A Valentin De Bortoli %A Arnaud Doucet %A Felipe Llinares-López %A Courtney Paquette %A Quentin Berthet %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-marion25a %I PMLR %P 1999--2007 %U https://proceedings.mlr.press/v258/marion25a.html %V 258 %X Sampling and automatic differentiation are both ubiquitous in modern machine learning. At its intersection, differentiating through a sampling operation, with respect to the parameters of the sampling process, is a problem that is both challenging and broadly applicable. We introduce a general framework and a new algorithm for first-order optimization of parameterized stochastic diffusions, performing 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 and experimental results showcasing the performance of our method.
APA
Marion, P., Korba, A., Bartlett, P., Blondel, M., Bortoli, V.D., Doucet, A., Llinares-López, F., Paquette, C. & Berthet, Q.. (2025). Implicit Diffusion: Efficient optimization through stochastic sampling. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:1999-2007 Available from https://proceedings.mlr.press/v258/marion25a.html.

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