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While diffusion models have shown great success in image generation, their noise-inverting generative process does not explicitly consider the structure of images, such as their inherent multi-scale nature. Inspired by diffusion models and…
Diffusion or flow-based models are powerful generative paradigms that are notoriously hard to sample as samples are defined as solutions to high-dimensional Ordinary or Stochastic Differential Equations (ODEs/SDEs) which require a large…
The field of numerical simulation is of significant importance for the design and management of real-world systems, with partial differential equations (PDEs) being a commonly used mathematical modeling tool. However, solving PDEs remains…
Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audios, and point clouds. Recently, the deep connection between forward-backward stochastic differential equations…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
In subsurface imaging, learning the mapping from velocity maps to seismic waveforms (forward problem) and waveforms to velocity (inverse problem) is important for several applications. While traditional techniques for solving forward and…
Despite the progress of learning-based methods for 6D object pose estimation, the trade-off between accuracy and scalability for novel objects still exists. Specifically, previous methods for novel objects do not make good use of the target…
Designing materials with targeted properties remains challenging due to the vastness of chemical space and the scarcity of property-labeled data. While recent advances in generative models offer a promising way for inverse design, most…
This paper presents PolyDiffuse, a novel structured reconstruction algorithm that transforms visual sensor data into polygonal shapes with Diffusion Models (DM), an emerging machinery amid exploding generative AI, while formulating…
Diffusion models are a powerful framework for tackling ill-posed problems, with recent advancements extending their use to point cloud upsampling. Despite their potential, existing diffusion models struggle with inefficiencies as they map…
Beyond estimating parameters of interest from data, one of the key goals of statistical inference is to properly quantify uncertainty in these estimates. In Bayesian inference, this uncertainty is provided by the posterior distribution, the…
We consider the inverse problem of estimating parameters of a driven diffusion (e.g., the underlying fluid flow, diffusion coefficient, or source terms) from point measurements of a passive scalar (e.g., the concentration of a pollutant).…
Neural operator surrogates for time-dependent partial differential equations (PDEs) conventionally employ autoregressive prediction schemes, which accumulate error over long rollouts and require uniform temporal discretization. We introduce…
We present DeepVekua, a hybrid architecture that unifies geometric deep learning with spectral analysis to solve partial differential equations (PDEs) in sparse data regimes. By learning a diffeomorphic coordinate transformation that maps…
Improving the quality of hyperspectral images (HSIs), such as through super-resolution, is a crucial research area. However, generative modeling for HSIs presents several challenges. Due to their high spectral dimensionality, HSIs are too…
The task of simultaneously reconstructing multiple physical coefficients in partial differential equations (PDEs) from observed data is ubiquitous in applications. In this work, we propose an integrated data-driven and model-based iterative…
Scene flow estimation, which aims to predict per-point 3D displacements of dynamic scenes, is a fundamental task in the computer vision field. However, previous works commonly suffer from unreliable correlation caused by locally constrained…
Score-based diffusion models in infinite-dimensional function spaces provide a mathematically principled framework for modelling function-valued data, offering key advantages such as resolution invariance and the ability to handle irregular…
Underwater visuals undergo various complex degradations, inevitably influencing the efficiency of underwater vision tasks. Recently, diffusion models were employed to underwater image enhancement (UIE) tasks, and gained SOTA performance.…
Inverse problems, which involve estimating parameters from incomplete or noisy observations, arise in various fields such as medical imaging, geophysics, and signal processing. These problems are often ill-posed, requiring regularization…