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Diffusion models (DMs) have exhibited remarkable efficacy in various image restoration tasks. However, existing approaches typically operate within the high-dimensional pixel space, resulting in high computational overhead. While methods…
We introduce Adjoint Sampling, a highly scalable and efficient algorithm for learning diffusion processes that sample from unnormalized densities, or energy functions. It is the first on-policy approach that allows significantly more…
The Arbitrary Linear Plasma Solver (ALPS) is a parallelised numerical code that solves the dispersion relation in a hot (even relativistic) magnetised plasma with an arbitrary number of particle species with arbitrary gyrotropic equilibrium…
Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…
Medical Imaging (MI) tasks, such as accelerated parallel Magnetic Resonance Imaging (MRI), often involve reconstructing an image from noisy or incomplete measurements. This amounts to solving ill-posed inverse problems, where a satisfactory…
Solving inverse problems with the reverse process of a diffusion model represents an appealing avenue to produce highly realistic, yet diverse solutions from incomplete and possibly noisy measurements, ultimately enabling uncertainty…
Ill-posed imaging inverse problems remain challenging due to the ambiguity in mapping degraded observations to clean images. Diffusion-based generative priors have recently shown promise, but typically rely on computationally intensive…
We present Automatic Laplace Collapsed Sampling (ALCS), a general framework for marginalising latent parameters in Bayesian models using automatic differentiation, which we combine with nested sampling to explore the hyperparameter space in…
Image restoration has experienced significant advancements due to the development of deep learning. Nevertheless, it encounters challenges related to ill-posed problems, resulting in deviations between single model predictions and…
Constructing fast samplers for unconditional diffusion and flow-matching models has received much attention recently; however, existing methods for solving inverse problems, such as super-resolution, inpainting, or deblurring, still require…
Score Distillation Sampling (SDS) has been pivotal for leveraging pre-trained diffusion models in downstream tasks such as inverse problems, but it faces two major challenges: $(i)$ mode collapse and $(ii)$ latent space inversion, which…
There is a growing interest in the use of latent diffusion models (LDMs) for image restoration (IR) tasks due to their ability to model effectively the distribution of natural images. While significant progress has been made, there are…
This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches -- which typically assume full knowledge of the forward model or access to paired degraded and…
Reconstructing the structure of thin films and multilayers from measurements of scattered X-rays or neutrons is key to progress in physics, chemistry, and biology. However, finding all structures compatible with reflectometry data is…
Recent advancements in diffusion models have been leveraged to address inverse problems without additional training, and Diffusion Posterior Sampling (DPS) (Chung et al., 2022a) is among the most popular approaches. Previous analyses…
Using diffusion models to solve inverse problems is a growing field of research. Current methods assume the degradation to be known and provide impressive results in terms of restoration quality and diversity. In this work, we leverage the…
This work addresses the recovery and demixing problem of signals that are sparse in some general dictionary. Involved applications include source separation, image inpainting, super-resolution, and restoration of signals corrupted by…
Diffusion models (DMs) have recently shown outstanding capabilities in modeling complex image distributions, making them expressive image priors for solving Bayesian inverse problems. However, most existing DM-based methods rely on…
A fundamental problem in modern supervised learning is computing reliable conditional prediction intervals in high-dimensional settings: existing methods often rely on restrictive modelling assumptions, do not scale as predictor dimension…
Learning diffusion bridge models is easy; making them fast and practical is an art. Diffusion bridge models (DBMs) are a promising extension of diffusion models for applications in image-to-image translation. However, like many modern…