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Modelling partial differential equations (PDEs) is of crucial importance in science and engineering, and it includes tasks ranging from forecasting to inverse problems, such as data assimilation. However, most previous numerical and machine…

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…

Inverse rendering, the process of inferring scene properties from images, is a challenging inverse problem. The task is ill-posed, as many different scene configurations can give rise to the same image. Most existing solutions incorporate…

Diffusion models have shown remarkable success in visual synthesis, but have also raised concerns about potential abuse for malicious purposes. In this paper, we seek to build a detector for telling apart real images from…

Diffusion model-based inverse problem solvers have demonstrated state-of-the-art performance in cases where the forward operator is known (i.e. non-blind). However, the applicability of the method to blind inverse problems has yet to be…

Diffusion models have quickly risen in popularity for their ability to model complex distributions and perform effective posterior sampling. Unfortunately, the iterative nature of these generative models makes them computationally expensive…

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…

Diffusion models have impressive image generation capability, but low-quality generations still exist, and their identification remains challenging due to the lack of a proper sample-wise metric. To address this, we propose BayesDiff, a…

Diffusion models have been used as priors for solving inverse problems. However, existing approaches typically overlook side information that could significantly improve reconstruction quality, especially in severely ill-posed settings. In…

Bayesian statistical inverse problems are often solved with Markov chain Monte Carlo (MCMC)-type schemes. When the problems are governed by large-scale discrete nonlinear partial differential equations (PDEs), they are computationally…

In medicine, treatments often influence multiple, interdependent outcomes, such as primary endpoints, complications, adverse events, or other secondary endpoints. Hence, to make optimal treatment decisions, clinicians are interested in…

Deconvolution of astronomical images is a key aspect of recovering the intrinsic properties of celestial objects, especially when considering ground-based observations. This paper explores the use of diffusion models (DMs) and the Diffusion…

Conventional score-based diffusion models (DMs) may struggle with anisotropic Gaussian diffusion processes due to the required inversion of covariance matrices in the denoising score matching training objective…

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 task of counterfactual estimation from observational imaging data given a known causal structure. In particular, quantifying the causal effect of interventions for high-dimensional data with neural networks remains an open…

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift…

Current deep learning-based solutions for image analysis tasks are commonly incapable of handling problems to which multiple different plausible solutions exist. In response, posterior-based methods such as conditional Diffusion Models and…

Diffusion models are a special type of generative model, capable of synthesising new data from a learnt distribution. We introduce DISPR, a diffusion-based model for solving the inverse problem of three-dimensional (3D) cell shape…

Diffusion probabilistic models have demonstrated an outstanding capability to model natural images and raw audio waveforms through a paired diffusion and reverse processes. The unique property of the reverse process (namely, eliminating…

We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…