Related papers: A Gradient Flow Approach to Solving Inverse Proble…

Image generative models, particularly diffusion-based models, have surged in popularity due to their remarkable ability to synthesize highly realistic images. However, since these models are data-driven, they inherit biases from the…

Distillation addresses the slow sampling problem in diffusion models by creating models with smaller size or fewer steps that approximate the behavior of high-step teachers. In this work, we propose a reinforcement learning based…

Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process 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…

In the field of inverse estimation for systems modeled by partial differential equations (PDEs), challenges arise when estimating high- (or even infinite-) dimensional parameters. Typically, the ill-posed nature of such problems…

We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent…

Diffusion models have revolutionized generative tasks through high-fidelity outputs, yet flow matching (FM) offers faster inference and empirical performance gains. However, current foundation FM models are computationally prohibitive for…

Suppose X is a multivariate diffusion process that is observed discretely in time. At each observation time, a transformation of the state of the process is observed with noise. The smoothing problem consists of recovering the path of the…

From a Bayesian perspective, score-based diffusion solves inverse problems through joint inference, embedding the likelihood with the prior to guide the sampling process. However, this formulation fails to explain its practical behavior:…

Diffusion models are extensively used for modeling image priors for inverse problems. We introduce \emph{Diff-Unfolding}, a principled framework for learning posterior score functions of \emph{conditional diffusion models} by explicitly…

Diffusion models (DMs) have emerged as powerful generative models for solving inverse problems, offering a good approximation of prior distributions of real-world image data. Typically, diffusion models rely on large-scale clean signals to…

We study ``nonlocal diffusion equations'' of the form \[ \partial_{t}\frac{d\rho_{t}}{d\pi}(x)+\int_{X}\left(\frac{d\rho_{t}}{d\pi}(x)-\frac{d\rho_{t}}{d\pi}(y)\right)\eta(x,y)d\pi(y)=0\qquad(\dagger) \] where $X$ is either $\mathbb{R}^{d}$…

Diffusion models have demonstrated empirical successes in various applications and can be adapted to task-specific needs via guidance. This paper studies a form of gradient guidance for adapting a pre-trained diffusion model towards…

Large-scale diffusion models have achieved remarkable performance in generative tasks. Beyond their initial training applications, these models have proven their ability to function as versatile plug-and-play priors. For instance, 2D…

Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is…

Diffusion models have emerged as a powerful foundation model for visual generations. With an appropriate sampling process, it can effectively serve as a generative prior for solving general inverse problems. Current posterior sampling-based…

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…

Diffusion-based generative models represent a forefront direction in generative AI research today. Recent studies in physics have suggested that the renormalization group (RG) can be conceptualized as a diffusion process. This insight…

Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic…

Can a diffusion model trained on bedrooms recover human faces? Diffusion models are widely used as priors for inverse problems, but standard approaches usually assume a high-fidelity model trained on data that closely match the unknown…