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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…

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…

Inverse problems exist in many disciplines of science and engineering. In computer vision, for example, tasks such as inpainting, deblurring, and super resolution can be effectively modeled as inverse problems. Recently, denoising diffusion…

Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior…

Recent studies demonstrate that diffusion models can serve as a strong prior for solving inverse problems. A prominent example is Diffusion Posterior Sampling (DPS), which approximates the posterior distribution of data given the measure…

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are…

With the rapid development of diffusion models and flow-based generative models, there has been a surge of interests in solving noisy linear inverse problems, e.g., super-resolution, deblurring, denoising, colorization, etc, with generative…

Reconstructing PDE solutions from sparse observations is a core challenge in scientific computing. We present FM4PDE, a flow-matching generative framework that learns the joint distribution of PDE coefficients (or initial states) and…

Pretrained diffusion models are effective priors for Bayesian inverse problems, but posterior sampling with these priors is often costly because data-consistency guidance is applied throughout the full reverse trajectory. Existing methods…

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…

Diffusion models have gained attention for their ability to represent complex distributions and incorporate uncertainty, making them ideal for robust predictions in the presence of noisy or incomplete data. In this study, we develop and…

Denoising diffusion models are a powerful type of generative models used to capture complex distributions of real-world signals. However, their applicability is limited to scenarios where training samples are readily available, which is not…

Diffusion models have shown impressive results in generating high-quality conditional samples using guidance techniques such as Classifier-Free Guidance (CFG). However, existing methods often require additional training or neural function…

Solving partial differential equations (PDEs) on fine spatio-temporal scales for high-fidelity solutions is critical for numerous scientific breakthroughs. Yet, this process can be prohibitively expensive, owing to the inherent complexities…

Diffusion models have recently exhibited remarkable abilities to synthesize striking image samples since the introduction of denoising diffusion probabilistic models (DDPMs). Their key idea is to disrupt images into noise through a fixed…

Diffusion models excel at capturing the natural design spaces of images, molecules, DNA, RNA, and protein sequences. However, rather than merely generating designs that are natural, we often aim to optimize downstream reward functions while…

We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward…

Diffusion Probabilistic Models (DPMs) suffer from inefficient inference due to their slow sampling and high memory consumption, which limits their applicability to various medical imaging applications. In this work, we propose a novel…

We propose a simple, efficient, yet powerful framework for dense visual predictions based on the conditional diffusion pipeline. Our approach follows a "noise-to-map" generative paradigm for prediction by progressively removing noise from a…

Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential…