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$\infty$-Diff: Infinite Resolution Diffusion with Subsampled Mollified States
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Introduces ∞-Diff, a Gaussian diffusion model in Hilbert space trained on randomly subsampled coordinates, using mollified states and a multi-scale sparse-convolution plus grid architecture to generate arbitrary-resolution images.
Problem
Existing infinite-dimensional (neural field) generative models rely on point-wise functions conditioned on compressed latents, which limits sample quality and scaling to high resolution.
Approach
Define a diffusion process directly in L2 function space with mollified noise and states, and parameterise the denoiser with non-local integral operators (sparse convolutions on raw subsampled coordinates plus a grid U-Net) so that no latent compression is needed and the same model samples at any resolution.
Key results
- FID_CLIP of 4.57 on CelebA-HQ-64, 3.02 on CelebA-HQ-128, 3.87 on FFHQ-256 and 10.36 on LSUN Church-256, beating other infinite-dimensional methods (GASP, GEM, DPF, D2F).
- At 256x256 with 4x subsampling, training speedup is 1.4x; memory reductions up to 3.9x are reported for fixed batch size in the appendix tables.
- Samples trained at 256x256 can be generated at 64 to 1024 resolution; FFHQ-trained model at 1024 gets FID_CLIP 15.84 on 5000 samples.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Train on fewer sampled coordinates (ablation) | ∞-Diff · High-resolution image datasets | sample quality | Hurt |
| Train with 4× coordinate subsampling (ablation) | ∞-Diff · 256×256 images | training speedup: 1.4× | Helped |
| Use sparse downsampling instead of the multi-scale architecture's grid-based global aggregation (ablation) | ∞-Diff · Image generation | sample quality | Hurt |
| Use a spatially nonlinear kernel instead of a linear kernel (ablation) | ∞-Diff · Image generation | generalization | Hurt |
| Use Fourier Neural Operator architecture for the grid-based component instead of the selected convolutional architecture (ablation) | ∞-Diff · Image generation | sample quality | Hurt |
| Use v-prediction instead of mollified noise prediction (ablation) | ∞-Diff · Image generation | sample quality | Hurt |
| Use continuously parameterised kernels instead of bilinearly interpolated kernels (ablation) | ∞-Diff · Discretisation invariance | sample quality | Hurt |
Surprising findings
- Predicting mollified noise T*xi worked better than predicting x0 in the reported experiments.
- Uniformly sampled coordinates outperformed low-discrepancy sequences for approximating integrals.
Limitations
- Sparse operators do not yet perform well at higher sparsity; authors note future work needed for greater sparsity.
- Grid-based component is fixed at 128x128 resolution, so resolution changes rely mainly on sparse operators.
- Super-resolution via encoder loses information in the encoding process.
Experimental setup
Datasets: FFHQ LSUN Church CelebA-HQ
Benchmarks: CelebA-HQ 64x64 CelebA-HQ 128x128 FFHQ 256x256 LSUN Church 256x256
Metrics: FID_CLIP training speedup memory reduction
Baselines: CIPS StyleSwin UT StyleGAN2 D2F DPF GEM GASP
Builds on: DDPM DDIM Fourier Neural Operator diffusion autoencoders TorchSparse
Closest papers by meaning
- Diffusion Models Without Attention (CVPR 2024 · similarity 0.89)
- DiffFNO: Diffusion Fourier Neural Operator (CVPR 2025 · similarity 0.88)
- DCTdiff: Intriguing Properties of Image Generative Modeling in the DCT Space (ICML 2025 · similarity 0.88)
- FAM Diffusion: Frequency and Attention Modulation for High-Resolution Image Generation with Stable Diffusion (CVPR 2025 · similarity 0.88)
- Solving Diffusion ODEs with Optimal Boundary Conditions for Better Image Super-Resolution (ICLR 2024 · similarity 0.88)
- DisCo-Diff: Enhancing Continuous Diffusion Models with Discrete Latents (ICML 2024 · similarity 0.88)
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