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A recent line of research has exploited pre-trained generative diffusion models as priors for solving Bayesian inverse problems. We contribute to this research direction by designing a sequential Monte Carlo method for linear-Gaussian…
Geophysical inverse problems are often ill-posed and admit multiple solutions. Conventional discriminative methods typically yield a single deterministic solution, which fails to model the posterior distribution, cannot generate diverse…
We propose a general framework for conditional sampling in PDE-based inverse problems, targeting the recovery of whole solutions from extremely sparse or noisy measurements. This is accomplished by a function-space diffusion model and…
Diffusion models are the current state-of-the-art for solving inverse problems in imaging. Their impressive generative capability allows them to approximate sampling from a prior distribution, which alongside a known likelihood function…
We propose a data-efficient, physics-aware generative framework in function space for inverse PDE problems. Existing plug-and-play diffusion posterior samplers represent physics implicitly through joint coefficient-solution modeling,…
Divide-and-conquer MCMC is a strategy for parallelising Markov Chain Monte Carlo sampling by running independent samplers on disjoint subsets of a dataset and merging their output. An ongoing challenge in the literature is to efficiently…
Diffusion models have recently shown considerable potential in solving Bayesian inverse problems when used as priors. However, sampling from the resulting denoising posterior distributions remains a challenge as it involves intractable…
Diffusion probabilistic models (DPMs) are a key component in modern generative models. DPM-solvers have achieved reduced latency and enhanced quality significantly, but have posed challenges to find the exact inverse (i.e., finding the…
Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modeling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by…
In recent years we have witnessed a growth in mathematics for deep learning, which has been used to solve inverse problems of partial differential equations (PDEs). However, most deep learning-based inversion methods either require paired…
Diffusion models (DMs) have recently shown remarkable performance on inverse problems (IPs). Optimization-based methods can fast solve IPs using DMs as powerful regularizers, but they are susceptible to local minima and noise overfitting.…
Diffusion models have emerged as powerful generative priors for solving inverse imaging problems. However, their practical deployment is hindered by the substantial computational cost of slow, multi-step sampling. Although Consistency…
The choice of prior is central to solving ill-posed imaging inverse problems, making it essential to select one consistent with the measurements $y$ to avoid severe bias. In Bayesian inverse problems, this could be achieved by evaluating…
The methodology developed in this article is motivated by a wide range of prediction and uncertainty quantification problems that arise in Statistics, Machine Learning and Applied Mathematics, such as non-parametric regression, multi-class…
Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…
Inverse problems (IPs) involve reconstructing signals from noisy observations. Recently, diffusion models (DMs) have emerged as a powerful framework for solving IPs, achieving remarkable reconstruction performance. However, existing…
Diffusion models have made remarkable progress in solving various inverse problems, attributing to the generative modeling capability of the data manifold. Posterior sampling from the conditional score function enable the precious data…
The recent emergence of diffusion models has significantly advanced the precision of learnable priors, presenting innovative avenues for addressing inverse problems. Since inverse problems inherently entail maximum a posteriori estimation,…
Many inference problems involve inferring the number $N$ of components in some region, along with their properties $\{\mathbf{x}_i\}_{i=1}^N$, from a dataset $\mathcal{D}$. A common statistical example is finite mixture modelling. In the…
There has been a flurry of activity around using pretrained diffusion models as informed data priors for solving inverse problems, and more generally around steering these models using reward models. Training-free methods like diffusion…