# DiffPINN: Generative diffusion-initialized physics-informed neural networks for accelerating seismic wavefield representation

arXiv: https://arxiv.org/abs/2506.00471 · HTML: https://mlsanity.com/paper/2506.00471/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 8 of its 33 references that are in the map.
- First posted on arXiv 31 May 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 8 of 8)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [OpenFWI: Large-Scale Multi-Structural Benchmark Datasets for Seismic Full Waveform Inversion](https://mlsanity.com/paper/2111.02926/) (2021)
- [Neural Network Diffusion](https://mlsanity.com/paper/2402.13144/) (2024)
- [PINNup: Robust neural network wavefield solutions using frequency upscaling and neuron splitting](https://mlsanity.com/paper/2109.14536/) (2021)
- [Physics-informed neural wavefields with Gabor basis functions](https://mlsanity.com/paper/2310.10602/) (2023)
- [Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network](https://mlsanity.com/paper/2502.00897/) (2025)

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

- [PILD: Physics-Informed Learning via Diffusion](https://mlsanity.com/paper/2601.21284/) (2026)

## Abstract (arXiv)

Physics-informed neural networks (PINNs) offer a powerful framework for seismic wavefield modeling, yet they typically require time-consuming retraining when applied to different velocity models. Moreover, their training can suffer from slow convergence due to the complexity of of the wavefield solution. To address these challenges, we introduce a latent diffusion-based strategy for rapid and effective PINN initialization. First, we train multiple PINNs to represent frequency-domain scattered wavefields for various velocity models, then flatten each trained network's parameters into a one-dimensional vector, creating a comprehensive parameter dataset. Next, we employ an autoencoder to learn latent representations of these parameter vectors, capturing essential patterns across diverse PINN's parameters. We then train a conditional diffusion model to store the distribution of these latent vectors, with the corresponding velocity models serving as conditions. Once trained, this diffusion model can generate latent vectors corresponding to new velocity models, which are subsequently decoded by the autoencoder into complete PINN parameters. Experimental results indicate that our method significantly accelerates training and maintains high accuracy across in-distribution and out-of-distribution velocity scenarios.