Conditional score-based diffusion model (SBDM) is for conditional generation of target data with paired data as condition, and has achieved great success in image translation. However, it requires the paired data as condition, and there would be insufficient paired data provided in real-world applications.

Unpaired image-to-image translation (I2I) aims to transfer an image from a source domain to a related targetdomain, whichinvolvesawide range ofcomputer vision tasks such asstyle transfer, super-resolution and pose estimation [35]. InI2I, the translated image should berealistictofitthe style of the target domain by changing the domain-specific features accordingly, andfaithful to preservethedomain-independent featuresofthesourceimage.

Conditional score-based diffusion model (SBDM) is for conditional generation of target data with paired data as condition, and has achieved great success in image translation. However, it requires the paired data as condition, and there would be insufficient paired data provided in real-world applications. To tackle the applications with partially paired or even unpaired dataset, we propose a novel Optimal Transport-guided Conditional Score-based diffusion model (OTCS) in this paper. We build the coupling relationship for the unpaired or partially paired dataset based on $L_2$-regularized unsupervised or semi-supervised optimal transport, respectively. Based on the coupling relationship, we develop the objective for training the conditional score-based model for unpaired or partially paired settings, which is based on a reformulation and generalization of the conditional SBDM for paired setting. With the estimated coupling relationship, we effectively train the conditional score-based model by designing a ``resampling-by-compatibility'' strategy to choose the sampled data with high compatibility as guidance. Extensive experiments on unpaired super-resolution and semi-paired image-to-image translation demonstrated the effectiveness of the proposed OTCS model. From the viewpoint of optimal transport, OTCS provides an approach to transport data across distributions, which is a challenge for OT on large-scale datasets. We theoretically prove that OTCS realizes the data transport in OT with a theoretical bound.

Accurate forecasting of individualized, high-resolution cortical thickness (CTh) trajectories is essential for detecting subtle cortical changes, providing invaluable insights into neurodegenerative processes and facilitating earlier and more precise intervention strategies. However, CTh forecasting is a challenging task due to the intricate non-Euclidean geometry of the cerebral cortex and the need to integrate multi-modal data for subject-specific predictions. To address these challenges, we introduce the Spherical Brownian Bridge Diffusion Model (SBDM). Specifically, we propose a bidirectional conditional Brownian bridge diffusion process to forecast CTh trajectories at the vertex level of registered cortical surfaces. Our technical contribution includes a new denoising model, the conditional spherical U-Net (CoS-UNet), which combines spherical convolutions and dense cross-attention to integrate cortical surfaces and tabular conditions seamlessly. Compared to previous approaches, SBDM achieves significantly reduced prediction errors, as demonstrated by our experiments based on longitudinal datasets from the ADNI and OASIS. Additionally, we demonstrate SBDM's ability to generate individual factual and counterfactual CTh trajectories, offering a novel framework for exploring hypothetical scenarios of cortical development.

Conditional score-based diffusion model (SBDM) is for conditional generation of target data with paired data as condition, and has achieved great success in image translation. However, it requires the paired data as condition, and there would be insufficient paired data provided in real-world applications. To tackle the applications with partially paired or even unpaired dataset, we propose a novel Optimal Transport-guided Conditional Score-based diffusion model (OTCS) in this paper. We build the coupling relationship for the unpaired or partially paired dataset based on L_2 -regularized unsupervised or semi-supervised optimal transport, respectively. Based on the coupling relationship, we develop the objective for training the conditional score-based model for unpaired or partially paired settings, which is based on a reformulation and generalization of the conditional SBDM for paired setting.

Understanding local risks from extreme rainfall, such as flooding, requires both long records (to sample rare events) and high-resolution products (to assess localized hazards). Unfortunately, there is a dearth of long-record and high-resolution products that can be used to understand local risk and precipitation science. In this paper, we present a novel generative diffusion model that downscales (super-resolves) globally available Climate Prediction Center (CPC) gauge-based precipitation products and ERA5 reanalysis data to generate kilometer-scale precipitation estimates. Downscaling gauge-based precipitation from 55 km to 1 km while recovering extreme rainfall signals poses significant challenges. To enforce our model (named WassDiff) to produce well-calibrated precipitation intensity values, we introduce a Wasserstein Distance Regularization (WDR) term for the score-matching training objective in the diffusion denoising process. We show that WDR greatly enhances the model's ability to capture extreme values compared to diffusion without WDR. Extensive evaluation shows that WassDiff has better reconstruction accuracy and bias scores than conventional score-based diffusion models. Case studies of extreme weather phenomena, like tropical storms and cold fronts, demonstrate WassDiff's ability to produce appropriate spatial patterns while capturing extremes. Such downscaling capability enables the generation of extensive km-scale precipitation datasets from existing historical global gauge records and current gauge measurements in areas without high-resolution radar.