Related papers: Variational Diffusion Posterior Sampling with Midp…

Ill-posed inverse problems are fundamental in many domains, ranging from astrophysics to medical imaging. Emerging diffusion models provide a powerful prior for solving these problems. Existing maximum-a-posteriori (MAP) or posterior…

Existing image restoration methods mostly leverage the posterior distribution of natural images. However, they often assume known degradation and also require supervised training, which restricts their adaptation to complex real…

The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of…

This work introduces a new approximate proximal sampler that operates solely with zeroth-order information of the potential function. Prior theoretical analyses have revealed that proximal sampling corresponds to alternating forward and…

Diffusion models have recently gained prominence in offline reinforcement learning due to their ability to effectively learn high-performing, generalizable policies from static datasets. Diffusion-based planners facilitate long-horizon…

In recent years, denoising problems have become intertwined with the development of deep generative models. In particular, diffusion models are trained like denoisers, and the distribution they model coincide with denoising priors in the…

Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Mapping of often incomplete or degraded data to parameters is ill-posed, thus data-driven iterative solutions are required, for…

Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…

We study posterior sampling for inverse problems in discrete state spaces using discrete diffusion models as generative priors. While continuous diffusion models have become widely used for inverse problems, their discrete counterparts…

Recovering signals from low-order moments is a fundamental yet notoriously difficult task in inverse problems. This recovery process often reduces to solving ill-conditioned systems of polynomial equations. In this work, we propose a new…

Predicting potential outcomes of interventions from observational data is crucial for decision-making in medicine, but the task is challenging due to the fundamental problem of causal inference. Existing methods are largely limited to point…

The sparse structure of the solution for an inverse problem can be modelled using different sparsity enforcing priors when the Bayesian approach is considered. Analytical expression for the unknowns of the model can be obtained by building…

Conventional score-based diffusion models (DMs) may struggle with anisotropic Gaussian diffusion processes due to the required inversion of covariance matrices in the denoising score matching training objective…

Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…

In Bayesian inverse problems sampling the posterior distribution is often a challenging task when the underlying models are computationally intensive. To this end, surrogates or reduced models are often used to accelerate the computation.…

Score-based diffusion models demonstrate superior performance in generative tasks but encounter fundamental bottlenecks in inverse problems due to the analytical intractability of the time-dependent likelihood score. To bridge this gap, we…

We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices,…

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…

Continuous-time long-term event prediction plays an important role in many application scenarios. Most existing works rely on autoregressive frameworks to predict event sequences, which suffer from error accumulation, thus compromising…

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,…