SlowGuess/NeurIPS_2023_OCR huggingface dataset:
We visualize intermediate and final reconstruction samples for different algorithms in Figure 19. We see that DSBM-IPF and DSBM-IMF provide consistent samples with the low resolution source, whereas Diffusion-fb and Bridge Matching produce dissimilar samples. We also follow Bischoff and Deck (2023) for a more refined statistical analysis in Figures 20, 21, 22. DSBM-IMF achieves comparable performance as Diffusion-fb in terms of these statistical profiles, and can be comparatively more accurate e.g. in the tails of the distributions in Figure 20, and for the case  $k_{x} = k_{y} = 4$  in Figure 21 for which the power spectrum of supersaturation is correctly captured by DSBM-IMF but not by other methods. Comparing this analysis with Figure 11, DSBM-IMF is also significantly more accurate in terms of conditional consistency than Diffusion-fb. On the other hand, DSBM-IPF appears less accurate in terms of these unconditional statistics than Diffusion-fb and DSBM-IMF, but achieves lower  $\ell_{2}$  distances from the input sources in Figure 11. This suggests that DSBM-IPF and DSBM-IMF exhibit different empirical biases before convergence, and DSBM-IMF is more preferable when the accuracy of the samples are important. This is in line with IMF theory as the marginals  $\pi_0, \pi_T$  are preserved in IMF but not in IPF.
J Broader Impact
Our work focuses on theoretical and methodological research and is intended to bring closer the fields of generative modeling and optimal transport. It can be useful for learning transport maps between general distributions with high accuracy and high scalability, which can have useful applications
$^{10}$ https://github.com/CliMA/diffusion-bridge-downscaling (code released under Apache-2.0 license)
Figure 20: KDE estimates of values in supersaturation and vorticity fields.
Figure 21: Spectral density estimates of supersaturation and vorticity fields.
Figure 22: KDE estimates of spatial means of the supersaturation field. The shaded areas denote  $99\%$  confidence interval obtained using 10000 bootstrap samples.
in machine learning, but also natural science areas such as physics, biology and geosciences in which optimal transport maps with theoretical guarantees are appealing. Our fluid flows experiment demonstrates such potentials. However, as is the case for generative models as a whole, intentional malicious use could cause detrimental societal impacts.