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Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…

We explore the methodology and theory of reward-directed generation via conditional diffusion models. Directed generation aims to generate samples with desired properties as measured by a reward function, which has broad applications in…

We explore unsupervised speech enhancement using diffusion models as expressive generative priors for clean speech. Existing approaches guide the reverse diffusion process using noisy speech through an approximate, noise-perturbed…

Data imputation and data generation have important applications for many domains, like healthcare and finance, where incomplete or missing data can hinder accurate analysis and decision-making. Diffusion models have emerged as powerful…

Graphical lasso is one of the most used estimators for inferring genetic networks. Despite its diffusion, there are several fields in applied research where the limits of detection of modern measurement technologies make the use of this…

Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world…

Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely…

Diffusion models have become the go-to method for large-scale generative models in real-world applications. These applications often involve data distributions confined within bounded domains, typically requiring ad-hoc thresholding…

Diffusion models have emerged as powerful tools for high-quality image generation and editing, but guiding these models to produce specific outputs remains a challenge. Conventional approaches rely on conditioning mechanisms, such as text…

The problem of estimating censored linear regression models with autocorrelated errors arises in many environmental and social studies. The present work proposes a Bayesian approach to estimate censored regression models with AR(p) errors.…

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

Collaborative filtering is a critical technique in recommender systems. It has been increasingly viewed as a conditional generative task for user feedback data, where newly developed diffusion model shows great potential. However, existing…

While the mathematical foundations of score-based generative models are increasingly well understood for unconstrained Euclidean spaces, many practical applications involve data restricted to bounded domains. This paper provides a…

Monitoring microbiological behaviors in water is crucial to manage public health risk from waterborne pathogens, although quantifying the concentrations of microbiological organisms in water is still challenging because concentrations of…

Building on recent advances in image generation, we present a fully data-driven approach to rendering markup into images. The approach is based on diffusion models, which parameterize the distribution of data using a sequence of denoising…

Diffusion models have attracted a lot of attention in recent years. These models view speech generation as a continuous-time process. For efficient training, this process is typically restricted to additive Gaussian noising, which is…

Standard diffusion models involve an image transform -- adding Gaussian noise -- and an image restoration operator that inverts this degradation. We observe that the generative behavior of diffusion models is not strongly dependent on the…

Denoising diffusion models are a class of generative models which have recently achieved state-of-the-art results across many domains. Gradual noise is added to the data using a diffusion process, which transforms the data distribution into…

Linear regression is arguably the most prominent among statistical inference methods, popular both for its simplicity as well as its broad applicability. On par with data-intensive applications, the sheer size of linear regression problems…

As a key component of power system production simulation, load forecasting is critical for the stable operation of power systems. Machine learning methods prevail in this field. However, the limited training data can be a challenge. This…