Related papers: Variational Diffusion Posterior Sampling with Midp…
We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate…
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…
Inverse problems arise in a multitude of applications, where the goal is to recover a clean signal from noisy and possibly (non)linear observations. The difficulty of a reconstruction problem depends on multiple factors, such as the ground…
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…
Diffusion models have excellent capacity to model complex distributions of natural data, which has made them a popular and effective choice for posterior sampling in imaging inverse problems. Existing methods can incorporate any measurement…
Pre-trained diffusion models have been successfully used as priors in a variety of linear inverse problems, where the goal is to reconstruct a signal from noisy linear measurements. However, existing approaches require knowledge of the…
Score-based methods, such as diffusion models and Bayesian inverse problems, are often interpreted as learning the data distribution in the low-noise limit ($\sigma \to 0$). In this work, we propose an alternative perspective: their success…
Diffusion posterior sampling conditions diffusion priors on measurements, but data-consistency updates are typically scaled by hand-tuned guidance weights and can destabilize sampling under stiff, operator-dependent curvature. We replace…
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…
This paper studies the original discrete-time denoising diffusion probabilistic model (DDPM) from a probabilistic point of view. We present three main theoretical results. First, we show that the time-dependent score function associated…
Recent advancements in diffusion models have been effective in learning data priors for solving inverse problems. They leverage diffusion sampling steps for inducing a data prior while using a measurement guidance gradient at each step to…
Diffusion models are now commonly used to solve inverse problems in computational imaging. However, most diffusion-based inverse solvers require complete knowledge of the forward operator to be used. In this work, we introduce a novel…
Generative models have recently undergone significant advancement due to the diffusion models. The success of these models can be often attributed to their use of guidance techniques, such as classifier or classifier-free guidance, which…
Many interesting tasks in image restoration can be cast as linear inverse problems. A recent family of approaches for solving these problems uses stochastic algorithms that sample from the posterior distribution of natural images given the…
Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse…
A pre-trained unconditional diffusion model, combined with posterior sampling or maximum a posteriori (MAP) estimation techniques, can solve arbitrary inverse problems without task-specific training or fine-tuning. However, existing…
Many inference problems involve inferring the number $N$ of components in some region, along with their properties $\{\mathbf{x}_i\}_{i=1}^N$, from a dataset $\mathcal{D}$. A common statistical example is finite mixture modelling. In the…
Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…
Denoising diffusion models, a class of generative models, have garnered immense interest lately in various deep-learning problems. A diffusion probabilistic model defines a forward diffusion stage where the input data is gradually perturbed…
In this work, we study the problem of learning the volatility under market microstructure noise. Specifically, we consider noisy discrete time observations from a stochastic differential equation and develop a novel computational method to…