Related papers: ODE-DPS: ODE-based Diffusion Posterior Sampling fo…
Diffusion models have emerged as a powerful foundation model for visual generations. With an appropriate sampling process, it can effectively serve as a generative prior for solving general inverse problems. Current posterior sampling-based…
Existing approaches to diffusion-based inverse problem solvers frame the signal recovery task as a probabilistic sampling episode, where the solution is drawn from the desired posterior distribution. This framework suffers from several…
This paper approaches the unsupervised learning problem by gradient descent in the space of probability density functions. A main result shows that along the gradient flow induced by a distribution-dependent ordinary differential equation…
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…
We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…
Sampling invariant distributions from an It\^o diffusion process presents a significant challenge in stochastic simulation. Traditional numerical solvers for stochastic differential equations require both a fine step size and a lengthy…
We propose an end-to-end approach for solving inverse problems for a class of complex astronomical signals, namely Spectral Energy Distributions (SEDs). Our goal is to reconstruct such signals from scarce and/or unreliable measurements. We…
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…
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 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…
The pretrained diffusion model as a strong prior has been leveraged to address inverse problems in a zero-shot manner without task-specific retraining. Different from the unconditional generation, the measurement-guided generation requires…
In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the…
Existing diffusion-based methods for inverse problems sample from the posterior using score functions and accept the generated random samples as solutions. In applications that posterior mean is preferred, we have to generate multiple…
Deep Gaussian processes (DGPs) provide a robust paradigm for Bayesian deep learning. In DGPs, a set of sparse integration locations called inducing points are selected to approximate the posterior distribution of the model. This is done to…
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…
Robust Bayesian inference using density power divergence (DPD) has emerged as a promising approach for handling outliers in statistical estimation. Although the DPD-based posterior offers theoretical guarantees of robustness, its practical…
Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions. While such models have achieved…
The choice of prior is central to solving ill-posed imaging inverse problems, making it essential to select one consistent with the measurements $y$ to avoid severe bias. In Bayesian inverse problems, this could be achieved by evaluating…
While diffusion models have shown great success in image generation, their noise-inverting generative process does not explicitly consider the structure of images, such as their inherent multi-scale nature. Inspired by diffusion models and…
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,…