User-defined Event Sampling and Uncertainty Quantification in Diffusion Models for Physical Dynamical Systems
This work addresses the problem of accurately modeling extreme events and uncertainties in physical systems for researchers and practitioners in fields like climate science or engineering, representing an incremental improvement over existing methods.
The paper tackles the challenge of conditional sampling and uncertainty quantification in diffusion models for chaotic dynamical systems, developing a probabilistic approximation scheme for the conditional score function that enables sampling on user-defined events and matches data statistics, including in distribution tails.
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 userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.