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Sampling from Diffusion Models can alternatively be seen as solving differential equations, where there is a challenge in balancing speed and image visual quality. ODE-based samplers offer rapid sampling time but reach a performance limit,…

Recovering true signals from noisy measurements is a central challenge in inverse problems spanning medical imaging, geophysics, and signal processing. Current methods balance prior signal priors (regularization) with agreement with noisy…

Remote sensing imagery is essential for environmental monitoring, agricultural management, and disaster response. However, data loss due to cloud cover, sensor failures, or incomplete acquisition-especially in high-resolution and…

Stochastic differential equations (SDEs) are a fundamental tool for modelling dynamic processes, including gene regulatory networks (GRNs), contaminant transport, financial markets, and image generation. However, learning the underlying SDE…

Acquiring high-quality data for training discriminative models is a crucial yet challenging aspect of building effective predictive systems. In this paper, we present Diffusion Inversion, a simple yet effective method that leverages the…

We introduce and analyze a novel class of inverse problems for stochastic dynamics: Given the ergodic invariant measure of a stochastic process governed by a nonlinear stochastic ordinary or partial differential equation (SODE or SPDE), we…

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…

Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints.…

Deconvolution of astronomical images is a key aspect of recovering the intrinsic properties of celestial objects, especially when considering ground-based observations. This paper explores the use of diffusion models (DMs) and the Diffusion…

Text-to-image diffusion models have recently attracted the interest of many researchers, and inverting the diffusion process can play an important role in better understanding the generative process and how to engineer prompts in order to…

We consider the inverse problem of reconstructing the scattering and absorption coefficients using boundary measurements for a time dependent radiative transfer equation (RTE). As the measurement is mostly polluted by errors, both…

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…

This paper considers the problem of utilizing a large-scale text-to-image diffusion model to tackle the challenging Inexact Segmentation (IS) task. Unlike traditional approaches that rely heavily on discriminative-model-based paradigms or…

Diffusion models (DMs) create samples from a data distribution by starting from random noise and iteratively solving a reverse-time ordinary differential equation (ODE). Because each step in the iterative solution requires an expensive…

Diffusion or score-based models recently showed high performance in image generation. They rely on a forward and a backward stochastic differential equations (SDE). The sampling of a data distribution is achieved by numerically solving the…

The success of denoising diffusion models raises important questions regarding their generalisation behaviour, particularly in high-dimensional settings. Notably, it has been shown that when training and sampling are performed perfectly,…

Diffusion models have been firmly established as principled zero-shot solvers for linear and nonlinear inverse problems, owing to their powerful image prior and iterative sampling algorithm. These approaches often rely on Tweedie's formula,…

Reconstructing 3D objects from extremely sparse views is a long-standing and challenging problem. While recent techniques employ image diffusion models for generating plausible images at novel viewpoints or for distilling pre-trained…

Diffusion-based generative models are extremely effective in generating high-quality images, with generated samples often surpassing the quality of those produced by other models under several metrics. One distinguishing feature of these…

Diffusion bridge models establish probabilistic paths between arbitrary paired distributions and exhibit great potential for universal image restoration. Most existing methods merely treat them as simple variants of stochastic interpolants,…