∞-Diff: Infinite Resolution Diffusion with Subsampled Mollified States

Bond-Taylor, Sam; Willcocks, Chris G.

Abstract

This paper introduces ∞-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× 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.

Citation

Bond-Taylor, S., & Willcocks, C. G. (2024, May). ∞-Diff: Infinite Resolution Diffusion with Subsampled Mollified States. Presented at The International Conference on Learning Representations (ICLR), Vienna Austria

• Presentation Conference Type: Conference Paper (published)
• Conference Name: The International Conference on Learning Representations (ICLR)
• Start Date: May 7, 2024
• End Date: May 11, 2024
• Acceptance Date: Jan 16, 2024
• Deposit Date: Mar 14, 2024
• Peer Reviewed: Peer Reviewed
• Book Title: The Twelfth International Conference on Learning Representations
• Public URL: https://durham-repository.worktribe.com/output/2328620
• Publisher URL: https://openreview.net/forum?id=OUeIBFhyem
• Related Public URLs: https://iclr.cc/; https://iclr.cc/virtual/2024/poster/18741; https://doi.org/10.48550/arXiv.2303.18242