# Blurring Diffusion Models

arXiv: https://arxiv.org/abs/2209.05557 · HTML: https://mlsanity.com/paper/2209.05557/

## Key facts

- Cited by 91 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 21 references that are in the map.
- First posted on arXiv 12 Sep 2022.

## 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)
- [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 Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [DeblurGAN: Blind Motion Deblurring Using Conditional Adversarial Networks](https://mlsanity.com/paper/1711.07064/) (2017)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Deblurring via Stochastic Refinement](https://mlsanity.com/paper/2112.02475/) (2021)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [Lossy Compression with Gaussian Diffusion](https://mlsanity.com/paper/2206.08889/) (2022)
- [Universal Speech Enhancement with Score-based Diffusion](https://mlsanity.com/paper/2206.03065/) (2022)
- [Subspace Diffusion Generative Models](https://mlsanity.com/paper/2205.01490/) (2022)
- [Progressive Deblurring of Diffusion Models for Coarse-to-Fine Image Synthesis](https://mlsanity.com/paper/2207.11192/) (2022)

## Built on by (most cited first, 30 of 91)

- [PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers](https://mlsanity.com/paper/2308.05732/) (2023)
- [DiffRF: Rendering-Guided 3D Radiance Field Diffusion](https://mlsanity.com/paper/2212.01206/) (2022)
- [Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration](https://mlsanity.com/paper/2303.11435/) (2023)
- [Improving Sample Quality of Diffusion Models Using Self-Attention Guidance](https://mlsanity.com/paper/2210.00939/) (2022)
- [Denoising Diffusion Samplers](https://mlsanity.com/paper/2302.13834/) (2023)
- [ConsistI2V: Enhancing Visual Consistency for Image-to-Video Generation](https://mlsanity.com/paper/2402.04324/) (2024)
- [DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting](https://mlsanity.com/paper/2306.01984/) (2023)
- [Minimizing Trajectory Curvature of ODE-based Generative Models](https://mlsanity.com/paper/2301.12003/) (2023)
- [Variational Flow Matching for Graph Generation](https://mlsanity.com/paper/2406.04843/) (2024)
- [Score-based Diffusion Models in Function Space](https://mlsanity.com/paper/2302.07400/) (2023)
- [Relay Diffusion: Unifying diffusion process across resolutions for image synthesis](https://mlsanity.com/paper/2309.03350/) (2023)
- [Multiscale Structure Guided Diffusion for Image Deblurring](https://mlsanity.com/paper/2212.01789/) (2022)
- [Diffusion Models for Black-Box Optimization](https://mlsanity.com/paper/2306.07180/) (2023)
- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [Consistent Diffusion Models: Mitigating Sampling Drift by Learning to be Consistent](https://mlsanity.com/paper/2302.09057/) (2023)
- [Diffusion Models With Learned Adaptive Noise](https://mlsanity.com/paper/2312.13236/) (2023)
- [Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modelling](https://mlsanity.com/paper/2404.12940/) (2024)
- [f-DM: A Multi-stage Diffusion Model via Progressive Signal Transformation](https://mlsanity.com/paper/2210.04955/) (2022)
- [Spectral Diffusion Processes](https://mlsanity.com/paper/2209.14125/) (2022)
- [∞-Diff: Infinite Resolution Diffusion with Subsampled Mollified States](https://mlsanity.com/paper/2303.18242/) (2023)
- [Neural Diffusion Models](https://mlsanity.com/paper/2310.08337/) (2023)
- [Warped Diffusion: Solving Video Inverse Problems with Image Diffusion Models](https://mlsanity.com/paper/2410.16152/) (2024)
- [Learning to Jump: Thinning and Thickening Latent Counts for Generative Modeling](https://mlsanity.com/paper/2305.18375/) (2023)
- [Beta Diffusion](https://mlsanity.com/paper/2309.07867/) (2023)
- [DiffEnc: Variational Diffusion with a Learned Encoder](https://mlsanity.com/paper/2310.19789/) (2023)
- [Improved Order Analysis and Design of Exponential Integrator for Diffusion Models Sampling](https://mlsanity.com/paper/2308.02157/) (2023)
- [Renormalizing Diffusion Models](https://mlsanity.com/paper/2308.12355/) (2023)
- [DiracDiffusion: Denoising and Incremental Reconstruction with Assured Data-Consistency](https://mlsanity.com/paper/2303.14353/) (2023)
- [Star-Shaped Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2302.05259/) (2023)
- [Generative Fractional Diffusion Models](https://mlsanity.com/paper/2310.17638/) (2023)

## Abstract (arXiv)

Recently, Rissanen et al., (2022) have presented a new type of diffusion process for generative modeling based on heat dissipation, or blurring, as an alternative to isotropic Gaussian diffusion. Here, we show that blurring can equivalently be defined through a Gaussian diffusion process with non-isotropic noise. In making this connection, we bridge the gap between inverse heat dissipation and denoising diffusion, and we shed light on the inductive bias that results from this modeling choice. Finally, we propose a generalized class of diffusion models that offers the best of both standard Gaussian denoising diffusion and inverse heat dissipation, which we call Blurring Diffusion Models.