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

Part of Advances in Neural Information Processing Systems 36 (NeurIPS 2023) Main Conference Track

Bibtex Paper Supplemental


Zhong Yi Wan, Ricardo Baptista, Anudhyan Boral, Yi-Fan Chen, John Anderson, Fei Sha, Leonardo Zepeda-Núñez


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 bycomposing 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: