Related papers: A Gradient Flow Approach to Solving Inverse Proble…
We study image inverse problems with a normalizing flow prior. Our formulation views the solution as the maximum a posteriori estimate of the image conditioned on the measurements. This formulation allows us to use noise models with…
This paper is devoted to the investigation of the backward problem for a multi-term time-fractional diffusion equation. Backward problems for fractional diffusion equations are typically studied using regularization methods due to their…
We develop in this paper a new regularized flow dynamic approach to construct efficient numerical schemes for Wasserstein gradient flows in Lagrangian coordinates. Instead of approximating the Wasserstein distance which needs to solve…
Diffusion and flow-based generative models have achieved remarkable success in domains such as image synthesis, video generation, and natural language modeling. In this work, we extend these advances to weight space learning by leveraging…
Diffusion models have shown significant progress in image translation tasks recently. However, due to their stochastic nature, there's often a trade-off between style transformation and content preservation. Current strategies aim to…
Used as priors for Bayesian inverse problems, diffusion models have recently attracted considerable attention in the literature. Their flexibility and high variance enable them to generate multiple solutions for a given task, such as…
Obtaining samples from the posterior distribution of inverse problems with expensive forward operators is challenging especially when the unknowns involve the strongly heterogeneous Earth. To meet these challenges, we propose a…
Recent advancements in solving Bayesian inverse problems have spotlighted denoising diffusion models (DDMs) as effective priors. Although these have great potential, DDM priors yield complex posterior distributions that are challenging to…
A conditional latent-diffusion based framework for solving the electromagnetic inverse scattering problem associated with microwave imaging is introduced. This generative machine-learning model explicitly mirrors the non-uniqueness of the…
The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…
Wasserstein Gradient Flow (WGF) describes the gradient dynamics of probability density within the Wasserstein space. WGF provides a promising approach for conducting optimization over the probability distributions. Numerically approximating…
Methods based on diffusion models (DMs) for solving inverse problems (IPs) have recently achieved remarkable performance. However, DM-based methods typically struggle against outliers, which are common in real-world measurements. In this…
Efficient sampling of complex data distributions can be achieved using trained invertible flows (IF), where the model distribution is generated by pushing a simple base distribution through multiple non-linear bijective transformations.…
Diffusion models have achieved remarkable success in imaging inverse problems owing to their powerful generative capabilities. However, existing approaches typically rely on models trained for specific degradation types, limiting their…
Full waveform inversion (FWI) has the potential to provide high-resolution subsurface model estimations. However, due to limitations in observation, e.g., regional noise, limited shots or receivers, and band-limited data, it is hard to…
When solving inverse problems, one increasingly popular approach is to use pre-trained diffusion models as plug-and-play priors. This framework can accommodate different forward models without re-training while preserving the generative…
Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…
We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we…
We present a latent diffusion-based differentiable inversion method (LD-DIM) for PDE-constrained inverse problems involving high-dimensional spatially distributed coefficients. LD-DIM couples a pretrained latent diffusion prior with an…
Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…