# Diffusion prior as a direct regularization term for FWI

arXiv: https://arxiv.org/abs/2506.10141 · HTML: https://mlsanity.com/paper/2506.10141/

## Key facts

- Cited by 2 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 14 of its 29 references that are in the map.
- First posted on arXiv 11 Jun 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, 14 of 14)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing](https://mlsanity.com/paper/2407.01521/) (2024)
- [Stochastic seismic waveform inversion using generative adversarial networks as a geological prior](https://mlsanity.com/paper/1806.03720/) (2018)
- [From GAN to WGAN](https://mlsanity.com/paper/1904.08994/) (2019)
- [A prior regularized full waveform inversion using generative diffusion models](https://mlsanity.com/paper/2306.12776/) (2023)
- [Total-variation regularization strategies in full-waveform inversion](https://mlsanity.com/paper/1608.06159/) (2016)
- [Controllable seismic velocity synthesis using generative diffusion models](https://mlsanity.com/paper/2402.06277/) (2024)
- [Sparse-promoting Full Waveform Inversion based on Online Orthonormal Dictionary Learning](https://mlsanity.com/paper/1511.05194/) (2015)
- [A stable deep adversarial learning approach for geological facies generation](https://mlsanity.com/paper/2305.13318/) (2023)
- [Stochastic full waveform inversion with deep generative prior for uncertainty quantification](https://mlsanity.com/paper/2406.04859/) (2024)

## Built on by (most cited first, 2 of 2)

- [Decoupled Latent Optimization of Diffusion Models for Full Waveform Inversion](https://mlsanity.com/paper/2606.14139/) (2026)
- [Physical-State-Guided Diffusion Sampling for Full-Waveform Inversion](https://mlsanity.com/paper/2609.12899/) (2026)

## Abstract (arXiv)

Diffusion models have recently shown promise as powerful generative priors for inverse problems. However, conventional applications require solving the full reverse diffusion process and operating on noisy intermediate states, which poses challenges for physics-constrained computational seismic imaging. In particular, such instability is pronounced in non-linear solvers like those used in Full Waveform Inversion (FWI), where wave propagation through noisy velocity fields can lead to numerical artifacts and poor inversion quality. In this work, we propose a simple yet effective framework that directly integrates a pretrained Denoising Diffusion Probabilistic Model (DDPM) as a score-based generative diffusion prior into FWI through a score rematching strategy. Unlike traditional diffusion approaches, our method avoids the reverse diffusion sampling and needs fewer iterations. We operate the image inversion entirely in the clean image space, eliminating the need to operate through noisy velocity models. The generative diffusion prior can be introduced as a simple regularization term in the standard FWI update rule, requiring minimal modification to existing FWI pipelines. This promotes stable wave propagation and can improve convergence behavior and inversion quality. Numerical experiments suggest that the proposed method offers enhanced fidelity and robustness compared to conventional and GAN-based FWI approaches, while remaining practical and computationally efficient for seismic imaging and other inverse problem tasks.