# Non-Uniform Diffusion Models

arXiv: https://arxiv.org/abs/2207.09786 · HTML: https://mlsanity.com/paper/2207.09786/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 16 of its 29 references that are in the map.
- First posted on arXiv 20 Jul 2022.

## Placed in

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

## Builds on (most cited first, 16 of 16)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (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)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Holistically-Nested Edge Detection](https://mlsanity.com/paper/1504.06375/) (2015)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Hierarchical Conditional Flow: A Unified Framework for Image Super-Resolution and Image Rescaling](https://mlsanity.com/paper/2108.05301/) (2021)

## Built on by (most cited first, 14 of 14)

- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [DeepCache: Accelerating Diffusion Models for Free](https://mlsanity.com/paper/2312.00858/) (2023)
- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)
- [Towards Coherent Image Inpainting Using Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2304.03322/) (2023)
- [On the Design Fundamentals of Diffusion Models: A Survey](https://mlsanity.com/paper/2306.04542/) (2023)
- [Efficient Diffusion Models for Vision: A Survey](https://mlsanity.com/paper/2210.09292/) (2022)
- [Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generation](https://mlsanity.com/paper/2303.04772/) (2023)
- [Continuous Diffusion for Mixed-Type Tabular Data](https://mlsanity.com/paper/2312.10431/) (2023)
- [Zero-shot-Learning Cross-Modality Data Translation Through Mutual Information Guided Stochastic Diffusion](https://mlsanity.com/paper/2301.13743/) (2023)
- [CHIMLE: Conditional Hierarchical IMLE for Multimodal Conditional Image Synthesis](https://mlsanity.com/paper/2211.14286/) (2022)
- [Hierarchic Flows to Estimate and Sample High-dimensional Probabilities](https://mlsanity.com/paper/2405.03468/) (2024)
- [Variational Diffusion Auto-encoder: Latent Space Extraction from Pre-trained Diffusion Models](https://mlsanity.com/paper/2304.12141/) (2023)
- [The Interplay of Data Structure and Imbalance in the Learning Dynamics of Diffusion Models](https://mlsanity.com/paper/2605.06367/) (2026)
- [How Good Are Deep Generative Models for Solving Inverse Problems?](https://mlsanity.com/paper/2312.12691/) (2023)

## Abstract (arXiv)

Diffusion models have emerged as one of the most promising frameworks for deep generative modeling. In this work, we explore the potential of non-uniform diffusion models. We show that non-uniform diffusion leads to multi-scale diffusion models which have similar structure to this of multi-scale normalizing flows. We experimentally find that in the same or less training time, the multi-scale diffusion model achieves better FID score than the standard uniform diffusion model. More importantly, it generates samples 4.4 times faster in 128× 128 resolution. The speed-up is expected to be higher in higher resolutions where more scales are used. Moreover, we show that non-uniform diffusion leads to a novel estimator for the conditional score function which achieves on par performance with the state-of-the-art conditional denoising estimator. Our theoretical and experimental findings are accompanied by an open source library MSDiff which can facilitate further research of non-uniform diffusion models.