Scientific discovery and engineering design are currently limited by the time and cost of
physical experiments. Numerical simulations are an alternative approach but are usually …

Common image-to-image translation methods rely on joint training over data from both
source and target domains. The training process requires concurrent access to both …

Modern generative models exhibit unprecedented capabilities to generate extremely
realistic data. However, given the inherent compositionality of real world, reliable use of …

Diffusion models have made rapid progress in generating high-quality samples across
various domains. However, a theoretical understanding of the Lipschitz continuity and …

Abstract We introduce Functional Diffusion Processes (FDPs), which generalize score-
based diffusion models to infinite-dimensional function spaces. FDPs require a new …

Denoising diffusion models have proven to be a flexible and effective paradigm for
generative modelling. Their recent extension to infinite dimensional Euclidean spaces has …

We propose functional diffusion a generative diffusion model focused on infinite-
dimensional function data samples. In contrast to previous work functional diffusion works on …

Score-based diffusion models (SBDM) have recently emerged as state-of-the-art
approaches for image generation. Existing SBDMs are typically formulated in a finite …

Diffusion models have had a profound impact on many application areas, including those
where data are intrinsically infinite-dimensional, such as images or time series. The …

This paper introduces $\infty $-Diff, a generative diffusion model defined in an infinite-
dimensional Hilbert space, which can model infinite resolution data. By training on randomly …