# Beyond Blur: A Fluid Perspective on Generative Diffusion Models

arXiv: https://arxiv.org/abs/2506.16827 · HTML: https://mlsanity.com/paper/2506.16827/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 32 of its 44 references that are in the map.
- First posted on arXiv 20 Jun 2025.

## Placed in

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

## Builds on (most cited first, 30 of 32)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [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)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [On the Importance of Noise Scheduling for Diffusion Models](https://mlsanity.com/paper/2301.10972/) (2023)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [Soft Diffusion: Score Matching for General Corruptions](https://mlsanity.com/paper/2209.05442/) (2022)
- [Blurring Diffusion Models](https://mlsanity.com/paper/2209.05557/) (2022)
- [Blue noise for diffusion models](https://mlsanity.com/paper/2402.04930/) (2024)
- [XLB: A differentiable massively parallel lattice Boltzmann library in Python](https://mlsanity.com/paper/2311.16080/) (2023)

## Built on by (most cited first, 1 of 1)

- [Multi-Scale Generative Modeling with Heat Dissipation Flow Matching](https://mlsanity.com/paper/2605.19371/) (2026)

## Abstract (arXiv)

We propose a novel PDE-driven corruption process for generative image synthesis based on advection-diffusion processes which generalizes existing PDE-based approaches. Our forward pass formulates image corruption via a physically motivated PDE that couples directional advection with isotropic diffusion and Gaussian noise, controlled by dimensionless numbers (Peclet, Fourier). We implement this PDE numerically through a GPU-accelerated custom Lattice Boltzmann solver for fast evaluation. To induce realistic turbulence, we generate stochastic velocity fields that introduce coherent motion and capture multi-scale mixing. In the generative process, a neural network learns to reverse the advection-diffusion operator thus constituting a novel generative model. We discuss how previous methods emerge as specific cases of our operator, demonstrating that our framework generalizes prior PDE-based corruption techniques. We illustrate how advection improves the diversity and quality of the generated images while keeping the overall color palette unaffected. This work bridges fluid dynamics, dimensionless PDE theory, and deep generative modeling, offering a fresh perspective on physically informed image corruption processes for diffusion-based synthesis.