User-defined Event Sampling and Uncertainty Quantification in Diffusion Models for Physical Dynamical Systems

Marc Finzi, Anudhyan Boral, Andrew Gordon Wilson, Fei Sha, Leonardo Zepeda-Núñez

Research output: Contribution to journalConference articlepeer-review


Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear user-defined events at inference time, and matches data statistics even when sampling from the tails of the distribution.

Original languageEnglish (US)
Pages (from-to)10136-10152
Number of pages17
JournalProceedings of Machine Learning Research
StatePublished - 2023
Event40th International Conference on Machine Learning, ICML 2023 - Honolulu, United States
Duration: Jul 23 2023Jul 29 2023

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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