Beyond Blur: A Fluid Perspective on Generative Diffusion Models

ICCV 2025

Grzegorz Gruszczynski1,2, Jakub Jerzy Meixner1,3, Michal Jan Wlodarczyk1,4, Przemyslaw Musialski1,5,6
1IDEAS NCBR, 2Samsung AI Center Warsaw, 3Institute of Physics of Polish Academy of Sciences 4Warsaw University of Technology, 5IDEAS Research Institute, 6New Jersey Institute of Technology
Paper arXiv
Method comparison.

BeyondBlur generalizes existing approaches and proposes a new physics inspired way to think about corruption.

Abstract

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 (Péclet, 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 based inverse problems.

Contribution

(a) Input, (b) Advection (conservative), (c) Diffusion (conservative), (d) Gaussian noise (non-conservative)
Interpretation. (a) shows the input intensity profile. (b) Advection moves intensity between locations without changing the total amount (conservative). (c) Diffusion blurs intensity between neighbors, also conservative. (d) Gaussian noise increases or decreases intensity locally (non-conservative).

We design a PDE-based forward corruption process for diffusion models that combines directional advection, isotropic diffusion, and a small Gaussian perturbation. The image field \(u(x,y,t)\) evolves according to,

\( \dfrac{\partial u}{\partial t} + \nabla\!\cdot\!(v\,u) \;=\; \nabla\!\cdot(\alpha\,\nabla u) \;+\; \dot{Q}(t) \). Where:
  • Advection, \(\nabla\!\cdot(vu)\) — rearrange intensities in a spatially coherent way as dictated by an external velocity field, \(v\), which inherently preserves the global “mass” (color sum).
  • Diffusion,\(\nabla\!\cdot(\alpha\nabla u)\) — blurs local variations, also conservative.
  • Reaction, \( \dot Q(t) \) — a Gaussian noise.

In the forward corruption process, the turbulent advection induces variability in the trajectory by other means than traditional Gaussian noise. This produces directional, flow-like texture shifts beyond what isotropic blur can achieve. The Gaussian noise is added just before passing data to the neural network to regularize training, while keeping the forward process physically consistent. Therefore the global color palette is preserved by design.

We solve the PDE numerically using a GPU-accelerated Lattice Boltzmann Method (LBM), which efficiently handles the coupled advection-diffusion dynamics at image scale. Advection is driven by a spectrally generated turbulent velocity field with controllable multi-scale energy. The resolution-independent control of flow patterns is enabled by two similarity numbers:

  • Fourier number (Fo) — dimensionless time.
  • Péclet number (Pe) — dimensionless ratio of advection to diffusion.

When \( \mathrm{Pe}=0 \), the method reduces to prior isotropic PDE-based corruptions (e.g., heat-equation blur), making our approach a superset of earlier models.

BibTeX

@article{gruszczynski2025blurfluidperspectivegenerative
  author    = {Grzegorz Gruszczynski and Jakub J Meixner and Michal Jan Wlodarczyk and Przemyslaw Musialski},
  title     = {Beyond Blur: A Fluid Perspective on Generative Diffusion Models},
  journal   = {ICCV},
  year      = {2025},
}