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We present Bayesian Diffusion Models (BDM), a prediction algorithm that performs effective Bayesian inference by tightly coupling the top-down (prior) information with the bottom-up (data-driven) procedure via joint diffusion processes. We…

Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with…

Sequential probabilistic inference from streaming observations requires modeling distributions over future trajectories as new observations arrive. Although diffusion and flow-matching models are effective at capturing high-dimensional,…

Diffusion models have impressive image generation capability, but low-quality generations still exist, and their identification remains challenging due to the lack of a proper sample-wise metric. To address this, we propose BayesDiff, a…

Diffusion models have recently driven significant breakthroughs in generative modeling. While state-of-the-art models produce high-quality samples on average, individual samples can still be low quality. Detecting such samples without human…

Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality.…

Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior…

Bayesian inference is a popular approach to calibrating uncertainties, but it can underpredict such uncertainties when model misspecification is present, impacting its reliability to inform decision making. Recently, the statistics and…

Diffusion models (DMs) are capable of generating remarkably high-quality samples by iteratively denoising a random vector, a process that corresponds to moving along the probability flow ordinary differential equation (PF ODE).…

Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…

Computational imaging is crucial in many disciplines from autonomous driving to life sciences. However, traditional model-driven and iterative methods consume large computational power and lack scalability for imaging. Deep learning (DL) is…

We derive a novel generative model from iterative Gaussian posterior inference. By treating the generated sample as an unknown variable, we can formulate the sampling process in the language of Bayesian probability. Our model uses a…

Wall-bounded turbulent flows are chaotic and multiscale, rendering real-time prediction at high Reynolds numbers computationally prohibitive in applications such as wind farms. Classical data assimilation methods are based on repeated…

We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we…

We address the problem of data augmentation in a rotating turbulence set-up, a paradigmatic challenge in geophysical applications. The goal is to reconstruct information in two-dimensional (2D) cuts of the three-dimensional flow fields,…

Optimizing high-dimensional and complex black-box functions is crucial in numerous scientific applications. While Bayesian optimization (BO) is a powerful method for sample-efficient optimization, it struggles with the curse of…

Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…

Deep generative models have made rapid progress in image, text, audio, and video generation, and are increasingly being applied to structured records. For tabular data, however, generative modeling remains difficult: a dataset may contain…

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…

Diffusion Probabilistic Models (DPMs) are powerful generative models that have achieved unparalleled success in a number of generative tasks. In this work, we aim to build inductive biases into the training and sampling of diffusion models…