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Recent work on diffusion models proposed that they operate in two regimes: memorization, in which models reproduce their training data, and generalization, in which they generate novel samples. While this has been tested in high-noise…

We consider the problem of inferring high-dimensional data $\mathbf{x}$ in a model that consists of a prior $p(\mathbf{x})$ and an auxiliary differentiable constraint $c(\mathbf{x},\mathbf{y})$ on $x$ given some additional information…

Denoising Diffusion Probabilistic Models (DDPMs) provide the foundation for the recent breakthroughs in generative modeling. Their Markovian structure makes it difficult to define DDPMs with distributions other than Gaussian or discrete. In…

Advances in microscopy imaging enable researchers to visualize structures at the nanoscale level thereby unraveling intricate details of biological organization. However, challenges such as image noise, photobleaching of fluorophores, and…

Diffusion models are powerful generative models that map noise to data using stochastic processes. However, for many applications such as image editing, the model input comes from a distribution that is not random noise. As such, diffusion…

Diffusion probabilistic models have been successfully used to generate data from noise. However, most diffusion models are computationally expensive and difficult to interpret with a lack of theoretical justification. Random feature models…

Diffusion probabilistic models have made their way into a number of high-profile applications since their inception. In particular, there has been a wave of research into using diffusion models in the prediction and design of biomolecular…

Most existing theoretical investigations of the accuracy of diffusion models, albeit significant, assume the score function has been approximated to a certain accuracy, and then use this a priori bound to control the error of generation.…

Diffusion models for image generation often exhibit a trade-off between perceptual sample quality and data likelihood: training objectives emphasizing high-noise denoising steps yield realistic images but poor likelihoods, whereas…

Diffusion models are at the vanguard of generative AI research with renowned solutions such as ImageGen by Google Brain and DALL.E 3 by OpenAI. Nevertheless, the potential merits of diffusion models for communication engineering…

The ongoing technological revolution in measurement systems enables the acquisition of high-resolution samples in fields such as engineering, biology, and medicine. However, these observations are often subject to errors from measurement…

We introduce Transfusion, a recipe for training a multi-modal model over discrete and continuous data. Transfusion combines the language modeling loss function (next token prediction) with diffusion to train a single transformer over…

Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a…

Curse of Dimensionality is an unavoidable challenge in statistical probability models, yet diffusion models seem to overcome this limitation, achieving impressive results in high-dimensional data generation. Diffusion models assume that…

Denoising is intuitively related to projection. Indeed, under the manifold hypothesis, adding random noise is approximately equivalent to orthogonal perturbation. Hence, learning to denoise is approximately learning to project. In this…

The creativity of diffusion models refers to their ability to generate highly realistic images that are different from their training data. Creativity is somewhat surprising since it is known that if the denoiser used in the diffusion model…

Model-based reinforcement learning methods often use learning only for the purpose of estimating an approximate dynamics model, offloading the rest of the decision-making work to classical trajectory optimizers. While conceptually simple,…

Diffusion Models are probabilistic models that create realistic samples by simulating the diffusion process, gradually adding and removing noise from data. These models have gained popularity in domains such as image processing, speech…

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…

Along with recent diffusion models, randomized smoothing has become one of a few tangible approaches that offers adversarial robustness to models at scale, e.g., those of large pre-trained models. Specifically, one can perform randomized…