Related papers: Posterior sampling via Langevin dynamics based on …

Efficient Boltzmann-sampling using first-principles methods is challenging for extended systems due to the steep scaling of electronic structure methods with the system size. Stochastic approaches provide a gentler system-size dependency at…

Image recovery from compressive measurements requires a signal prior for the images being reconstructed. Recent work has explored the use of deep generative models with low latent dimension as signal priors for such problems. However, their…

Over the past decade, Plug-and-Play (PnP) has become a popular method for reconstructing images using a modular framework consisting of a forward and prior model. The great strength of PnP is that an image denoiser can be used as a prior…

Inverse problems are prevalent in both scientific research and engineering applications. In the context of Bayesian inverse problems, sampling from the posterior distribution can be particularly challenging when the forward models are…

Large denoising diffusion models, such as Stable Diffusion, have been trained on billions of image-caption pairs to perform text-conditioned image generation. As a byproduct of this training, these models have acquired general knowledge…

This report studies diffusion posterior sampling (DPS) for single-image super-resolution (SISR) under a known degradation model. We implement a likelihood-guided sampling procedure that combines an unconditional diffusion prior with…

We propose a generative multivariate posterior sampler via flow matching. It offers a simple training objective, and does not require access to likelihood evaluation. The method learns a dynamic, block-triangular velocity field in the joint…

Solving image inverse problems (e.g., super-resolution and inpainting) requires generating a high fidelity image that matches the given input (the low-resolution image or the masked image). By using the input image as guidance, we can…

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…

The problem of efficiently generating random samples from high-dimensional and non-log-concave posterior measures arising from nonlinear regression problems is considered. Extending investigations from arXiv:2009.05298, local and global…

Sampling the parameter space of artificial neural networks according to a Boltzmann distribution provides insight into the geometry of low-loss solutions and offers an alternative to conventional loss minimization for training. However,…

Diffusion models have achieved remarkable progress in universal image restoration. While existing methods speed up inference by reducing sampling steps, substantial step intervals often introduce cumulative errors. Moreover, they struggle…

In the context of solving inverse problems for physics applications within a Bayesian framework, we present a new approach, Markov Chain Generative Adversarial Neural Networks (MCGANs), to alleviate the computational costs associated with…

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…

The deep image prior was recently introduced as a prior for natural images. It represents images as the output of a convolutional network with random inputs. For "inference", gradient descent is performed to adjust network parameters to…

Bayesian neural learning feature a rigorous approach to estimation and uncertainty quantification via the posterior distribution of weights that represent knowledge of the neural network. This not only provides point estimates of optimal…

Models of physics beyond the Standard Model often contain a large number of parameters. These form a high-dimensional space that is computationally intractable to fully explore. Experimental constraints project onto a subspace of viable…

Diffusion models have emerged as powerful learned priors for solving inverse problems. However, current iterative solving approaches which alternate between diffusion sampling and data consistency steps typically require hundreds or…

We propose a new class of generative models that naturally handle data of varying dimensionality by jointly modeling the state and dimension of each datapoint. The generative process is formulated as a jump diffusion process that makes…

Phase retrieval is an ill-posed inverse problem in which classical and deep learning-based methods struggle to jointly achieve measurement fidelity and perceptual realism. We propose a novel framework for phase retrieval that leverages…