Related papers: PnP-CM: Consistency Models as Plug-and-Play Priors…

Inverse design refers to the problem of optimizing the input of an objective function in order to enact a target outcome. For many real-world engineering problems, the objective function takes the form of a simulator that predicts how the…

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,…

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 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,…

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…

A standard model for image reconstruction involves the minimization of a data-fidelity term along with a regularizer, where the optimization is performed using proximal algorithms such as ISTA and ADMM. In plug-and-play (PnP)…

Diffusion models (DMs) are a powerful generative framework that have attracted significant attention in recent years. However, the high computational cost of training DMs limits their practical applications. In this paper, we start with a…

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…

Flow matching is a recent state-of-the-art framework for generative modeling based on ordinary differential equations (ODEs). While closely related to diffusion models, it provides a more general perspective on generative modeling. Although…

We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical…

Recently, diffusion models have achieved significant advances in vision, text, and robotics. However, they still face slow generation speeds due to sequential denoising processes. To address this, a parallel sampling method based on Picard…

The past few years have seen a surge of activity around integration of deep learning networks and optimization algorithms for solving inverse problems. Recent work on plug-and-play priors (PnP), regularization by denoising (RED), and deep…

Diffusion models have been recently studied as powerful generative inverse problem solvers, owing to their high quality reconstructions and the ease of combining existing iterative solvers. However, most works focus on solving simple linear…

Consistency models (CMs) offer faster sampling than traditional diffusion models, but their training is resource-intensive. For example, as of 2024, training a state-of-the-art CM on CIFAR-10 takes one week on 8 GPUs. In this work, we…

Physics informed neural networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems for PDEs. We focus on a particular class of inverse problems, the so-called data assimilation or unique…

Regularized inversion methods for image reconstruction are used widely due to their tractability and ability to combine complex physical sensor models with useful regularity criteria. Such methods motivated the recently developed…

Parameter estimation for differential equations from measured data is an inverse problem prevalent across quantitative sciences. Physics-Informed Neural Networks (PINNs) have emerged as effective tools for solving such problems, especially…

Diffusion models have recently demonstrated notable success in solving inverse problems. However, current diffusion model-based solutions typically require a large number of function evaluations (NFEs) to generate high-quality images…

Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of…

The plug-and-play (PnP) method uses a deep denoiser within a proximal algorithm for model-based image reconstruction (IR). Unlike end-to-end IR, PnP allows the same pretrained denoiser to be used across different imaging tasks, without the…