$\infty$-Diff: Infinite Resolution Diffusion with Subsampled Mollified States
This addresses the challenge of scaling generative models to infinite resolutions for applications like high-resolution image synthesis, though it is incremental as it builds on prior diffusion and neural field methods.
The paper tackles the problem of modeling infinite-resolution data with diffusion models by introducing $\infty$-Diff, which trains on randomly sampled subsets of coordinates to learn a continuous function for arbitrary resolution sampling, resulting in high-quality diffusion even at an 8× subsampling rate with lower FID scores and significant run-time and memory savings.
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.