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

arXiv:2303.18242v2 Announce Type: replace
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 …

abstract arxiv continuous cs.cv cs.lg data denoising diff diffusion diffusion model function generative learn locations paper prior sampling space subsets training type