(\infty\)-Diff: Infinite Resolution Diffusion with Subsampled Mollified States

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 sampled subsets of coordinates and denoising content only at those locations, we learn a continuous function for arb...

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Bibliographic Details
Published in:arXiv.org 2024-03
Main Authors: Bond-Taylor, Sam, Willcocks, Chris G
Format: Article
Language:English
Subjects:
Continuity (mathematics)
Diffusion
Sampling
Training
Online Access:Get full text
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Summary: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 sampled subsets of coordinates and denoising content only at those locations, we learn a continuous function for arbitrary resolution sampling. Unlike prior neural field-based infinite-dimensional models, which use point-wise functions requiring latent compression, our method employs non-local integral operators to map between Hilbert spaces, allowing spatial context aggregation. This is achieved with an efficient multi-scale function-space architecture that operates directly on raw sparse coordinates, coupled with a mollified diffusion process that smooths out irregularities. Through experiments on high-resolution datasets, we found that even at an \(8\times\) subsampling rate, our model retains high-quality diffusion. This leads to significant run-time and memory savings, delivers samples with lower FID scores, and scales beyond the training resolution while retaining detail.
ISSN:2331-8422