Related papers: Generative modelling with jump-diffusions

Bayesian models based on Gaussian processes (GPs) offer a flexible framework to predict spatially distributed variables with uncertainty. But the use of nonstationary priors, often necessary for capturing complex spatial patterns, makes…

While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in…

Generative modeling aims to transform random noise into structured outputs. In this work, we enhance video diffusion models by allowing motion control via structured latent noise sampling. This is achieved by just a change in data: we…

Flow-based generative models have recently shown impressive performance for conditional generation tasks, such as text-to-image generation. However, current methods transform a general unimodal noise distribution to a specific mode of the…

In this work we study how diffusion-based generative models produce high-dimensional data, such as an image, by implicitly relying on a manifestation of a low-dimensional set of latent abstractions, that guide the generative process. We…

We provide theoretical convergence guarantees for score-based generative models (SGMs) such as denoising diffusion probabilistic models (DDPMs), which constitute the backbone of large-scale real-world generative models such as DALL$\cdot$E…

Diffusion models have emerged as a powerful framework in generative modeling, typically relying on optimizing neural networks to estimate the score function via forward SDE simulations. In this work, we propose an alternative method that is…

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…

Score-based generative models (SGMs) sample from a target distribution by iteratively transforming noise using the score function of the perturbed target. For any finite training set, this score function can be evaluated in closed form, but…

While working within the spatial domain can pose problems associated with ill-conditioned scores caused by power-law decay, recent advances in diffusion-based generative models have shown that transitioning to the wavelet domain offers a…

Recently, score-based generative models have been successfully employed for the task of speech enhancement. A stochastic differential equation is used to model the iterative forward process, where at each step environmental noise and white…

We introduce and study a class of probabilistic generative models, where the latent object is a finite-dimensional diffusion process on a finite time interval and the observed variable is drawn conditionally on the terminal point of the…

Score-based diffusion models have significantly advanced generative deep learning for image processing. Measurement conditioned models have also been applied to inverse problems such as CT reconstruction. However, the conventional approach,…

Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the…

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…

Score-based generative models are a popular class of generative modelling techniques relying on stochastic differential equations (SDE). From their inception, it was realized that it was also possible to perform generation using ordinary…

Denoising diffusion models (DDMs) have recently attracted increasing attention by showing impressive synthesis quality. DDMs are built on a diffusion process that pushes data to the noise distribution and the models learn to denoise. In…

Diffusion models have become a leading paradigm in generative AI, with score estimation via denoising score matching as a central component. While recent theory provides strong statistical guarantees, it typically relies on…

Score-based generative models (SGMs) have revolutionized the field of generative modeling, achieving unprecedented success in generating realistic and diverse content. Despite empirical advances, the theoretical basis for why optimizing the…

Shot noise processes have been extensively studied due to their mathematical properties and their relevance in several applications. Here, we consider nonnegative shot noise processes and prove their weak convergence to L\'evy-driven…