Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Models

Published: 21 Sept 2023, Last Modified: 02 Nov 2023NeurIPS 2023 spotlightEveryoneRevisionsBibTeX
Keywords: optimal transport, probabilistic diffusion models, statistical downscaling
TL;DR: Two-stage framework for a probabilistic approach to statistical downscaling with unpaired data, using optimal transport for debiasing and probabilistic diffusion models for super-resolution.
Abstract: We introduce a two-stage probabilistic framework for statistical downscaling using unpaired data. Statistical downscaling seeks a probabilistic map to transform low-resolution data from a biased coarse-grained numerical scheme to high-resolution data that is consistent with a high-fidelity scheme. Our framework tackles the problem by composing two transformations: (i) a debiasing step via an optimal transport map, and (ii) an upsampling step achieved by a probabilistic diffusion model with a posteriori conditional sampling. This approach characterizes a conditional distribution without needing paired data, and faithfully recovers relevant physical statistics from biased samples. We demonstrate the utility of the proposed approach on one- and two-dimensional fluid flow problems, which are representative of the core difficulties present in numerical simulations of weather and climate. Our method produces realistic high-resolution outputs from low-resolution inputs, by upsampling resolutions of $8\times$ and $16\times$. Moreover, our procedure correctly matches the statistics of physical quantities, even when the low-frequency content of the inputs and outputs do not match, a crucial but difficult-to-satisfy assumption needed by current state-of-the-art alternatives. Code for this work is available at:
Supplementary Material: pdf
Submission Number: 10332