Related papers: Provable Diffusion Posterior Sampling for Bayesian…
Diffusion probabilistic models (DPMs) have emerged as a promising technique in generative modeling. The success of DPMs relies on two ingredients: time reversal of diffusion processes and score matching. In view of possibly unguaranteed…
We present a simple method to obtain optimal posterior distributions and improve the quality of Bayesian inference with reduced human and computational effort. Bayes' Theorem is reformulated in the language of statistical mechanics, wherein…
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…
Uncertainty quantification is crucial to inverse problems, as it could provide decision-makers with valuable information about the inversion results. For example, seismic inversion is a notoriously ill-posed inverse problem due to the…
We consider the problem of sampling from a distribution governed by a potential function. This work proposes an explicit score based MCMC method that is deterministic, resulting in a deterministic evolution for particles rather than a…
Physics-informed neural network (PINN) has been successfully applied in solving a variety of nonlinear non-convex forward and inverse problems. However, the training is challenging because of the non-convex loss functions and the multiple…
We introduce a numerical method for Brownian dynamics with position dependent diffusion tensor which is second order accurate for sampling the invariant measure while requiring only one force evaluation per timestep. Analysis of the…
Score based approaches to sampling have shown much success as a generative algorithm to produce new samples from a target density given a pool of initial samples. In this work, we consider if we have no initial samples from the target…
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"…
Recent advancements in diffusion models have been leveraged to address inverse problems without additional training, and Diffusion Posterior Sampling (DPS) (Chung et al., 2022a) is among the most popular approaches. Previous analyses…
Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and…
Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. In this paper, we reveal that recent methods can be uniformly interpreted as employing a…
Inverse problems exist in many disciplines of science and engineering. In computer vision, for example, tasks such as inpainting, deblurring, and super resolution can be effectively modeled as inverse problems. Recently, denoising diffusion…
We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent…
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…
Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
Sampling from an unknown distribution, accessible only through discrete samples, is a fundamental problem at the core of generative AI. The current state-of-the-art methods follow a two-step process: first, estimating the score function…
Recent studies on inverse problems have proposed posterior samplers that leverage the pre-trained diffusion models as powerful priors. These attempts have paved the way for using diffusion models in a wide range of inverse problems.…
Diffusion models have emerged as effective distribution estimators in vision, language, and reinforcement learning, but their use as priors in downstream tasks poses an intractable posterior inference problem. This paper studies amortized…