# ∞-Brush: Controllable Large Image Synthesis with Diffusion Models in Infinite Dimensions

arXiv: https://arxiv.org/abs/2407.14709 · HTML: https://mlsanity.com/paper/2407.14709/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 26 of its 33 references that are in the map.
- First posted on arXiv 20 Jul 2024.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 26 of 26)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [AudioLDM: Text-to-Audio Generation with Latent Diffusion Models](https://mlsanity.com/paper/2301.12503/) (2023)
- [MultiDiffusion: Fusing Diffusion Paths for Controlled Image Generation](https://mlsanity.com/paper/2302.08113/) (2023)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Quilt-1M: One Million Image-Text Pairs for Histopathology](https://mlsanity.com/paper/2306.11207/) (2023)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [Blurring Diffusion Models](https://mlsanity.com/paper/2209.05557/) (2022)
- [Matryoshka Diffusion Models](https://mlsanity.com/paper/2310.15111/) (2023)
- [Diffusion Generative Models in Infinite Dimensions](https://mlsanity.com/paper/2212.00886/) (2022)
- [Learned representation-guided diffusion models for large-image generation](https://mlsanity.com/paper/2312.07330/) (2023)
- [∞-Diff: Infinite Resolution Diffusion with Subsampled Mollified States](https://mlsanity.com/paper/2303.18242/) (2023)
- [MaskDiff: Modeling Mask Distribution with Diffusion Probabilistic Model for Few-Shot Instance Segmentation](https://mlsanity.com/paper/2303.05105/) (2023)

## Built on by (most cited first, 8 of 8)

- [ZoomLDM: Latent Diffusion Model for multi-scale image generation](https://mlsanity.com/paper/2411.16969/) (2024)
- [PixCell: A generative foundation model for digital histopathology images](https://mlsanity.com/paper/2506.05127/) (2025)
- [Gen-SIS: Generative Self-augmentation Improves Self-supervised Learning](https://mlsanity.com/paper/2412.01672/) (2024)
- [Functional Mean Flow in Hilbert Space](https://mlsanity.com/paper/2511.12898/) (2025)
- [FG-CXR: A Radiologist-Aligned Gaze Dataset for Enhancing Interpretability in Chest X-Ray Report Generation](https://mlsanity.com/paper/2411.15413/) (2024)
- [Hummingbird: High Fidelity Image Generation via Multimodal Context Alignment](https://mlsanity.com/paper/2502.05153/) (2025)
- [GazeSearch: Radiology Findings Search Benchmark](https://mlsanity.com/paper/2411.05780/) (2024)
- [STREAM: Stochastic Riemannian Flow Matching with Anisotropic Decoder for Digital Histopathology Image Generation](https://mlsanity.com/paper/2606.07036/) (2026)

## Abstract (arXiv)

Synthesizing high-resolution images from intricate, domain-specific information remains a significant challenge in generative modeling, particularly for applications in large-image domains such as digital histopathology and remote sensing. Existing methods face critical limitations: conditional diffusion models in pixel or latent space cannot exceed the resolution on which they were trained without losing fidelity, and computational demands increase significantly for larger image sizes. Patch-based methods offer computational efficiency but fail to capture long-range spatial relationships due to their overreliance on local information. In this paper, we introduce a novel conditional diffusion model in infinite dimensions, ∞-Brush for controllable large image synthesis. We propose a cross-attention neural operator to enable conditioning in function space. Our model overcomes the constraints of traditional finite-dimensional diffusion models and patch-based methods, offering scalability and superior capability in preserving global image structures while maintaining fine details. To our best knowledge, ∞-Brush is the first conditional diffusion model in function space, that can controllably synthesize images at arbitrary resolutions of up to 4096×4096 pixels. The code is available at https://github.com/cvlab-stonybrook/infinity-brush.