# Image Editing Models are Numerical Solvers

arXiv: https://arxiv.org/abs/2607.18787 · HTML: https://mlsanity.com/paper/2607.18787/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 60 references that are in the map.
- First posted on arXiv 21 Jul 2026.

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [InstructPix2Pix: Learning to Follow Image Editing Instructions](https://mlsanity.com/paper/2211.09800/) (2022)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [StyleCLIP: Text-Driven Manipulation of StyleGAN Imagery](https://mlsanity.com/paper/2103.17249/) (2021)
- [Blended Diffusion for Text-driven Editing of Natural Images](https://mlsanity.com/paper/2111.14818/) (2021)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [Designing an Encoder for StyleGAN Image Manipulation](https://mlsanity.com/paper/2102.02766/) (2021)
- [Paint by Example: Exemplar-based Image Editing with Diffusion Models](https://mlsanity.com/paper/2211.13227/) (2022)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [DiffusionPDE: Generative PDE-Solving Under Partial Observation](https://mlsanity.com/paper/2406.17763/) (2024)
- [VideoPDE: Unified Generative PDE Solving via Video Inpainting Diffusion Models](https://mlsanity.com/paper/2506.13754/) (2025)
- [Pretrained Video Models as Differentiable Physics Simulators for Urban Wind Flows](https://mlsanity.com/paper/2603.21210/) (2026)

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

- [Image-Space Rule Discovery](https://mlsanity.com/paper/2608.00490/) (2026)

## Abstract (arXiv)

We investigate whether a pretrained generative image-editing model can provide a common interface for numerical simulation. Physical inputs and solutions are rendered as images, while scalar quantities such as material properties, diffusivity, and loading parameters enter through lightweight adapters. Using established numerical and analytic solvers for supervision, we apply the same architecture and training protocol to heterogeneous elliptic equations, forced heat and Burgers evolution, complex Ginzburg-Landau dynamics, two-dimensional Navier-Stokes prediction, potential flow, elasticity, eikonal travel time, phase-field fracture, and entropic optimal transport. The results show that a pretrained image model can represent diverse static and time-dependent physical mappings, including unstable and shock-like behavior, when each task is expressed through a suitable visual encoding. This work is a capability study rather than an attempt to surpass specialized solvers. It also identifies fundamental constraints: image and latent representations complicate numerical range selection and direct enforcement of governing equations or invariants, while a failed Kuramoto-Sivashinsky experiment indicates that representation errors prevent meaningful long-horizon simulation of chaotic systems.