# $\\infty$-Diff: Infinite Resolution Diffusion with Subsampled Mollified States

Source: [$\\infty$-Diff: Infinite Resolution Diffusion with Subsampled Mollified States](<https://www.sota2.com/research/paper/68fa72581e209131cea55cf5>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-26T02:24:11.561Z

Authors: Sam Bond-Taylor, Chris G. Willcocks

Published: 2023-03-31T17:58:08.000Z

## Abstract

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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Spatiotemporal Field Reconstruction on Navier-Stokes (Full)](<https://www.sota2.com/research/sota/spatiotemporal-field-reconstruction-on-navier-stokes-full.md>): Spatiotemporal Field Reconstruction; Navier-Stokes (Full); CRPS: 0.2106.

- [Spatiotemporal Field Reconstruction on Navier-Stokes 10% Subset](<https://www.sota2.com/research/sota/spatiotemporal-field-reconstruction-on-navier-stokes-10-percent-subset.md>): Spatiotemporal Field Reconstruction; Navier-Stokes 10% Subset; CRPS: 0.461.

- [Spatiotemporal Forecasting on AirDelhi AD-B](<https://www.sota2.com/research/sota/spatiotemporal-forecasting-on-airdelhi-ad-b.md>): Spatiotemporal forecasting; AirDelhi AD-B; CRPS: 36.12.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2303.18242>)

[PDF](<https://arxiv.org/pdf/2303.18242.pdf>)