mlsanityData to 7 Oct 2026

∞-Diff: Infinite Resolution Diffusion with Subsampled Mollified States

arXiv 2303.18242 ↗First posted 31 Mar 2023cs.LG cs.CVcited by 21

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

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.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 61 of its 87 references that are in the map. First posted on arXiv 31 Mar 2023.

Builds on

61 of 87 references.

Closest ancestors · 21

Same direction, newest first

  1. 2023Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generation8 Mar
  2. 2023Consistency Models2 Mar
  3. 2023Continuous-Time Functional Diffusion Processes1 Mar
  4. 2023Diffusion Probabilistic Fields1 Mar
  5. 2023Score-based Diffusion Models in Function Space14 Feb
  6. 2023Simple diffusion: End-to-end diffusion for high resolution images26 Jan
  7. 2022Diffusion Generative Models in Infinite Dimensions1 Dec
  8. 2022Dimensionality-Varying Diffusion Process29 Nov
  9. 2022Blurring Diffusion Models12 Sep
  10. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  11. 2022Subspace Diffusion Generative Models3 May
  12. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
9 more
  1. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusion14 Dec
  2. 2021Diffusion Autoencoders: Toward a Meaningful and Decodable Representation30 Nov
  3. 2021Unleashing Transformers: Parallel Token Prediction with Discrete Absorbing Diffusion for Fast High-Resolution Image Generation from Vector-Quantized Codes24 Nov
  4. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  5. 2021Cascaded Diffusion Models for High Fidelity Image Generation30 May
  6. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  7. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  8. 2020Denoising Diffusion Implicit Models6 Oct
  9. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 40

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 4; 2024: 7; 2025: 6; 2026: 4.

21 papers.

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  1. 2024Make a Cheap Scaling: A Self-Cascade Diffusion Model for Higher-Resolution Adaptationcited by 50
  2. 2023Regularization by Texts for Latent Diffusion Inverse Solverscited by 31
  3. 2024Conditioning non-linear and infinite-dimensional diffusion processescited by 15
  4. 2023Functional Diffusioncited by 13
  5. 2023Manifold Diffusion Fieldscited by 11
  6. 2023Geometric Neural Diffusion Processescited by 10
  7. 2024∞-Brush: Controllable Large Image Synthesis with Diffusion Models in Infinite Dimensionscited by 8
  8. 2024Taming Score-Based Diffusion Priors for Infinite-Dimensional Nonlinear Inverse Problemscited by 7
  9. 2025Flow Matching Neural Processescited by 6
  10. 2025Preconditioned Langevin Dynamics with Score-Based Generative Models for Infinite-Dimensional Linear Bayesian Inverse Problemscited by 5
  11. 2025Flow Straight and Fast in Hilbert Space: Functional Rectified Flowcited by 5
  12. 2025Functional Mean Flow in Hilbert Spacecited by 5
9 more
  1. 2025Scale-Adaptive Generative Flows for Multiscale Scientific Datacited by 4
  2. 2024Learning Images Across Scales Using Adversarial Trainingcited by 3
  3. 2024INRFlow: Flow Matching for INRs in Ambient Spacecited by 2
  4. 2025Optimize Any Topology: A Foundation Model for Shape- and Resolution-Free Structural Topology Optimizationcited by 2
  5. 2026Dimension-Free Multimodal Sampling via Preconditioned Annealed Langevin Dynamicscited by 2
  6. 2026Trajectory Consistency for One-Step Generation on Euler Mean Flowscited by 2
  7. 2024Resolution-Robust 3D MRI Reconstruction with 2D Diffusion Priors: Diverse-Resolution Training Outperforms Interpolationcited by 1
  8. 2026Infinite dimensional generative sensingcited by 0
  9. 2026Dimension-Uniform Discretization Analysis of Preconditioned Annealed Langevin Dynamics for Multimodal Gaussian Mixturescited by 0

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  1. 2026DiffRGD: An Inference-Time Diffusion Guidance Through Riemannian Gradient Descent
  2. 2023Infinite-Dimensional Diffusion Models
  3. 2025Diffusion Generative Models Meet Compressed Sensing, with Applications to Imaging and Finance
  4. 2023Diffusion Models Without Attention
  5. 2025LowDiff: Efficient Diffusion Sampling with Low-Resolution Condition
  6. 2024I-Diff: Structural Regularization for High-Fidelity Diffusion Models
  7. 2025SlimDiff: Training-Free, Activation-Guided Hands-free Slimming of Diffusion Models
  8. 2023PartDiff: Image Super-resolution with Partial Diffusion Models