Beyond Blur: A Fluid Perspective on Generative Diffusion Models

2025-06-20

AI Summary

This work addresses the limitations of existing PDE-based image generation methods—namely, insufficient diversity, weak structural coherence, and poor physical interpretability—by proposing a physics-driven convection–diffusion generative framework. Methodologically, it introduces, for the first time, the fluid-dynamical convection–diffusion PDE into diffusion modeling, jointly incorporating directional convection, isotropic diffusion, and Gaussian noise, while augmenting texture diversity and structural consistency via a stochastic turbulent velocity field. The framework employs dimensionless modeling and a GPU-accelerated lattice Boltzmann solver, coupled with neural networks to learn the inverse evolution operator. Key contributions include: (i) unifying and generalizing mainstream PDE-based generative models—whose prior approaches emerge as special cases; (ii) significantly improving generation quality and diversity while preserving color fidelity; and (iii) empirically validating the framework’s generalizability and physical plausibility.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: Generation

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Web Mining and Content Analysis: Web data generation and simulation

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 (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.

Problem

• Generalizing PDE-based image corruption via advection-diffusion processes
• Reversing advection-diffusion operator for novel generative modeling
• Improving image diversity and quality with fluid dynamics principles

Innovation

• PDE-driven advection-diffusion for image synthesis
• GPU-accelerated Lattice Boltzmann solver implementation
• Neural network reverses advection-diffusion operator