# Resolution Chromatography of Diffusion Models

arXiv: https://arxiv.org/abs/2401.10247 · HTML: https://mlsanity.com/paper/2401.10247/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 23 of its 27 references that are in the map.
- First posted on arXiv 7 Dec 2023.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [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)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Fantasia3D: Disentangling Geometry and Appearance for High-quality Text-to-3D Content Creation](https://mlsanity.com/paper/2303.13873/) (2023)
- [DiffEdit: Diffusion-based semantic image editing with mask guidance](https://mlsanity.com/paper/2210.11427/) (2022)
- [Compositional Visual Generation with Composable Diffusion Models](https://mlsanity.com/paper/2206.01714/) (2022)
- [Score Jacobian Chaining: Lifting Pretrained 2D Diffusion Models for 3D Generation](https://mlsanity.com/paper/2212.00774/) (2022)
- [Simple diffusion: End-to-end diffusion for high resolution images](https://mlsanity.com/paper/2301.11093/) (2023)
- [Diffusion Models already have a Semantic Latent Space](https://mlsanity.com/paper/2210.10960/) (2022)
- [Perception Prioritized Training of Diffusion Models](https://mlsanity.com/paper/2204.00227/) (2022)
- [On the Importance of Noise Scheduling for Diffusion Models](https://mlsanity.com/paper/2301.10972/) (2023)
- [Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry](https://mlsanity.com/paper/2307.12868/) (2023)
- [Multiresolution Textual Inversion](https://mlsanity.com/paper/2211.17115/) (2022)

## Built on by (most cited first, 2 of 2)

- [Upsample Guidance: Scale Up Diffusion Models without Training](https://mlsanity.com/paper/2404.01709/) (2024)
- [NoiseShift: Resolution-Aware Noise Recalibration for Better Low-Resolution Image Generation](https://mlsanity.com/paper/2510.02307/) (2025)

## Abstract (arXiv)

Diffusion models generate high-resolution images through iterative stochastic processes. In particular, the denoising method is one of the most popular approaches that predicts the noise in samples and denoises it at each time step. It has been commonly observed that the resolution of generated samples changes over time, starting off blurry and coarse, and becoming sharper and finer. In this paper, we introduce "resolution chromatography" that indicates the signal generation rate of each resolution, which is very helpful concept to mathematically explain this coarse-to-fine behavior in generation process, to understand the role of noise schedule, and to design time-dependent modulation. Using resolution chromatography, we determine which resolution level becomes dominant at a specific time step, and experimentally verify our theory with text-to-image diffusion models. We also propose some direct applications utilizing the concept: upscaling pre-trained models to higher resolutions and time-dependent prompt composing. Our theory not only enables a better understanding of numerous pre-existing techniques for manipulating image generation, but also suggests the potential for designing better noise schedules.