# Diffusion Models Generate Images Like Painters: an Analytical Theory of Outline First, Details Later

arXiv: https://arxiv.org/abs/2303.02490 · HTML: https://mlsanity.com/paper/2303.02490/

## Key facts

- Cited by 55 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 19 of its 35 references that are in the map.
- First posted on arXiv 4 Mar 2023.

## Placed in

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

## Builds on (most cited first, 19 of 19)

- [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)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Poisson Flow Generative Models](https://mlsanity.com/paper/2209.11178/) (2022)
- [PFGM++: Unlocking the Potential of Physics-Inspired Generative Models](https://mlsanity.com/paper/2302.04265/) (2023)
- [PCA of high dimensional random walks with comparison to neural network training](https://mlsanity.com/paper/1806.08805/) (2018)

## Built on by (most cited first, 30 of 55)

- [Delta-DiT: A Training-Free Acceleration Method Tailored for Diffusion Transformers](https://mlsanity.com/paper/2406.01125/) (2024)
- [An analytic theory of creativity in convolutional diffusion models](https://mlsanity.com/paper/2412.20292/) (2024)
- [ReVersion: Diffusion-Based Relation Inversion from Images](https://mlsanity.com/paper/2303.13495/) (2023)
- [SG-I2V: Self-Guided Trajectory Control in Image-to-Video Generation](https://mlsanity.com/paper/2411.04989/) (2024)
- [A Dense Reward View on Aligning Text-to-Image Diffusion with Preference](https://mlsanity.com/paper/2402.08265/) (2024)
- [DenseDPO: Fine-Grained Temporal Preference Optimization for Video Diffusion Models](https://mlsanity.com/paper/2506.03517/) (2025)
- [The Unreasonable Effectiveness of Gaussian Score Approximation for Diffusion Models and its Applications](https://mlsanity.com/paper/2412.09726/) (2024)
- [Probing the Latent Hierarchical Structure of Data via Diffusion Models](https://mlsanity.com/paper/2410.13770/) (2024)
- [An Analytical Theory of Spectral Bias in the Learning Dynamics of Diffusion Models](https://mlsanity.com/paper/2503.03206/) (2025)
- [Generalization through variance: how noise shapes inductive biases in diffusion models](https://mlsanity.com/paper/2504.12532/) (2025)
- [Distilling Diversity and Control in Diffusion Models](https://mlsanity.com/paper/2503.10637/) (2025)
- [Diversity-Preserved Distribution Matching Distillation for Fast Visual Synthesis](https://mlsanity.com/paper/2602.03139/) (2026)
- [How Do Flow Matching Models Memorize and Generalize in Sample Data Subspaces?](https://mlsanity.com/paper/2410.23594/) (2024)
- [NewMove: Customizing text-to-video models with novel motions](https://mlsanity.com/paper/2312.04966/) (2023)
- [Understanding Representation Dynamics of Diffusion Models via Low-Dimensional Modeling](https://mlsanity.com/paper/2502.05743/) (2025)
- [DiverseGRPO: Mitigating Mode Collapse in Image Generation via Diversity-Aware GRPO](https://mlsanity.com/paper/2512.21514/) (2025)
- [The Hidden Linear Structure in Score-Based Models and its Application](https://mlsanity.com/paper/2311.10892/) (2023)
- [On the Interpolation Effect of Score Smoothing in Diffusion Models](https://mlsanity.com/paper/2502.19499/) (2025)
- [Token Perturbation Guidance for Diffusion Models](https://mlsanity.com/paper/2506.10036/) (2025)
- [A solvable model of learning generative diffusion: theory and insights](https://mlsanity.com/paper/2501.03937/) (2025)
- [Zo3T: Zero-Shot 3D-Aware Trajectory-Guided Image-to-Video Generation via Test-Time Training](https://mlsanity.com/paper/2509.06723/) (2025)
- [Effective Test-Time Scaling of Discrete Diffusion through Iterative Refinement](https://mlsanity.com/paper/2511.05562/) (2025)
- [Federated Learning for Diffusion Models](https://mlsanity.com/paper/2503.06426/) (2025)
- [Diffusion Classifiers Understand Compositionality, but Conditions Apply](https://mlsanity.com/paper/2505.17955/) (2025)
- [Pioneering 4-Bit FP Quantization for Diffusion Models: Mixup-Sign Quantization and Timestep-Aware Fine-Tuning](https://mlsanity.com/paper/2505.21591/) (2025)
- [Devil is in the Details: Density Guidance for Detail-Aware Generation with Flow Models](https://mlsanity.com/paper/2502.05807/) (2025)
- [Taming Flow-based I2V Models for Creative Video Editing](https://mlsanity.com/paper/2509.21917/) (2025)
- [Dark Noise Diffusion: Noise Synthesis for Low-Light Image Denoising](https://mlsanity.com/paper/2503.11262/) (2025)
- [Semantic Routing: Exploring Multi-Layer LLM Feature Weighting for Diffusion Transformers](https://mlsanity.com/paper/2602.03510/) (2026)
- [Diffusion Sampling Correction via Approximately 10 Parameters](https://mlsanity.com/paper/2411.06503/) (2024)

## Abstract (arXiv)

How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that underlies image generation has the following properties: (i) individual trajectories tend to be low-dimensional and resemble 2D `rotations'; (ii) high-variance scene features like layout tend to emerge earlier, while low-variance details tend to emerge later; and (iii) early perturbations tend to have a greater impact on image content than later perturbations. To understand these phenomena, we derive and study a closed-form solution to the probability flow ODE for a Gaussian distribution, which shows that the reverse diffusion state rotates towards a gradually-specified target on the image manifold. It also shows that generation involves first committing to an outline, and then to finer and finer details. We find that this solution accurately describes the initial phase of image generation for pretrained models, and can in principle be used to make image generation more efficient by skipping reverse diffusion steps. Finally, we use our solution to characterize the image manifold in Stable Diffusion. Our viewpoint reveals an unexpected similarity between generation by GANs and diffusion and provides a conceptual link between diffusion and image retrieval.