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Reversing a diffusion process by learning its score forms the heart of diffusion-based generative modeling and for estimating properties of scientific systems. The diffusion processes that are tractable center on linear processes with a…

Diffusion models have emerged as a powerful framework for generative tasks in deep learning. They decompose generative modeling into two computational primitives: deterministic neural-network evaluation and stochastic sampling. Current…

We aim to leverage diffusion to address the challenging image matting task. However, the presence of high computational overhead and the inconsistency of noise sampling between the training and inference processes pose significant obstacles…

Generative diffusion models, famous for their performance in image generation, are popular in various cross-domain applications. However, their use in the communication community has been mostly limited to auxiliary tasks like data modeling…

In recent years, diffusion models, and more generally score-based deep generative models, have achieved remarkable success in various applications, including image and audio generation. In this paper, we view diffusion models as an implicit…

Text-conditioned image generation models have recently shown immense qualitative success using denoising diffusion processes. However, unlike discriminative vision-and-language models, it is a non-trivial task to subject these…

We propose to use Gaussian process regression to accurately estimate the diffusion MRI signal at arbitrary locations in q-space. By estimating the signal on a grid, we can do synthetic diffusion spectrum imaging: reconstructing the ensemble…

Coherent ptychographic imaging experiments often discard over 99.9 % of the flux from a light source to define the coherence of an illumination. Even when coherent flux is sufficient, the stability required during an exposure is another…

Diffusion tensor imaging provides important information on tissue structure and orientation of fiber tracts in brain white matter in vivo. It results in diffusion tensors, which are $3\times3$ symmetric positive definite (SPD) matrices,…

Diffusion inversion is a task of recovering the noise of an image in a diffusion model, which is vital for controllable diffusion image editing. At present, diffusion inversion still remains a challenging task due to the lack of viable…

Diffusion Probabilistic Models (DPMs) have achieved strong generative performance, yet their inductive biases remain largely implicit. In this work, we aim to build inductive biases into the training and sampling of diffusion models to…

Errors in the data and the forward operator of an inverse problem can be handily modelled using partial order in Banach lattices. We present some existing results of the theory of regularisation in this novel framework, where errors are…

Modern data analyses frequently encounter settings where samples of variables are contaminated by measurement error. Ignoring measurement noise can substantially degrade statistical inference, while existing correction techniques are often…

Acquiring high-quality data for training discriminative models is a crucial yet challenging aspect of building effective predictive systems. In this paper, we present Diffusion Inversion, a simple yet effective method that leverages the…

We study the boundary trace processes of reflected diffusions on uniform domains. We obtain stable-like heat kernel estimates for such a boundary trace process when the diffusion on the underlying ambient space satisfies sub-Gaussian heat…

Diffusional Kurtosis Imaging (DKI) is a sensitive biomarker for microstructure in health and disease. However, DKI is not specific to any microstructural property since it may emerge from several different sources. Q-space trajectory…

Purpose: In diffusion MRI (dMRI), the volumetric and bundle analyses of whole-brain tissue microstructure and connectivity can be severely impeded by an incomplete field-of-view (FOV). This work aims to develop a method for imputing the…

Random sinusoidal features are a popular approach for speeding up kernel-based inference in large datasets. Prior to the inference stage, the approach suggests performing dimensionality reduction by first multiplying each data vector by a…

Diffusion Magnetic Resonance Imaging (dMRI) is a non-invasive tool for watching the microstructure of fibrous nerve and muscle tissue. From dMRI, it is possible to estimate 2-rank diffusion tensors imaging (DTI) fields, that are widely used…

We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an intrinsically low-dimensional manifold and…