# Controllable seismic velocity synthesis using generative diffusion models

arXiv: https://arxiv.org/abs/2402.06277 · HTML: https://mlsanity.com/paper/2402.06277/

## Key facts

- Cited by 13 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 28 of its 63 references that are in the map.
- First posted on arXiv 9 Feb 2024.

## 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, 28 of 28)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Is synthetic data from generative models ready for image recognition?](https://mlsanity.com/paper/2210.07574/) (2022)
- [Perception Prioritized Training of Diffusion Models](https://mlsanity.com/paper/2204.00227/) (2022)
- [Fast Sampling of Diffusion Models via Operator Learning](https://mlsanity.com/paper/2211.13449/) (2022)
- [InversionNet: A Real-Time and Accurate Full Waveform Inversion with CNNs and continuous CRFs](https://mlsanity.com/paper/1811.07875/) (2018)
- [Deep-learning inversion: a next generation seismic velocity-model building method](https://mlsanity.com/paper/1902.06267/) (2019)
- [Stochastic seismic waveform inversion using generative adversarial networks as a geological prior](https://mlsanity.com/paper/1806.03720/) (2018)
- [Conditional score-based diffusion models for Bayesian inference in infinite dimensions](https://mlsanity.com/paper/2305.19147/) (2023)
- [Deep-Learning Inversion of Seismic Data](https://mlsanity.com/paper/1901.07733/) (2019)
- [A prior regularized full waveform inversion using generative diffusion models](https://mlsanity.com/paper/2306.12776/) (2023)
- [Implicit Full Waveform Inversion with Deep Neural Representation](https://mlsanity.com/paper/2209.03525/) (2022)
- [WISE: full-Waveform variational Inference via Subsurface Extensions](https://mlsanity.com/paper/2401.06230/) (2023)
- [StorSeismic: A new paradigm in deep learning for seismic processing](https://mlsanity.com/paper/2205.00222/) (2022)
- [Seismic Data Interpolation via Denoising Diffusion Implicit Models with Coherence-corrected Resampling](https://mlsanity.com/paper/2307.04226/) (2023)
- [Data-driven Full-waveform Inversion Surrogate using Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2105.00100/) (2021)

## Built on by (most cited first, 13 of 13)

- [State-observation augmented diffusion model for nonlinear assimilation with unknown dynamics](https://mlsanity.com/paper/2407.21314/) (2024)
- [RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion](https://mlsanity.com/paper/2509.21659/) (2025)
- [Cross-Domain Foundation Model Adaptation: Pioneering Computer Vision Models for Geophysical Data Analysis](https://mlsanity.com/paper/2408.12396/) (2024)
- [A generative foundation model for an all-in-one seismic processing framework](https://mlsanity.com/paper/2502.01111/) (2025)
- [Robust Physics-Guided Diffusion for Full-Waveform Inversion](https://mlsanity.com/paper/2603.16393/) (2026)
- [Diffusion prior as a direct regularization term for FWI](https://mlsanity.com/paper/2506.10141/) (2025)
- [Diffusion Model-Based Posterior Sampling in Full Waveform Inversion](https://mlsanity.com/paper/2512.12797/) (2025)
- [Geological and Well prior assisted full waveform inversion using conditional diffusion models](https://mlsanity.com/paper/2412.06959/) (2024)
- [Power-scaled Bayesian Inference with Score-based Generative Models](https://mlsanity.com/paper/2504.10807/) (2025)
- [Diffusion models for multivariate subsurface generation and efficient probabilistic inversion](https://mlsanity.com/paper/2507.15809/) (2025)
- [Diffusion-based subsurface CO2 multiphysics monitoring and forecasting](https://mlsanity.com/paper/2407.18426/) (2024)
- [Acoustic Waveform Inversion with Image-to-Image Schr"odinger Bridges](https://mlsanity.com/paper/2506.15346/) (2025)
- [Is Artificial Intelligence Reshaping the Landscape of the International Academic Community of Geosciences?](https://mlsanity.com/paper/2508.20117/) (2025)

## Abstract (arXiv)

Accurate seismic velocity estimations are vital to understanding Earth's subsurface structures, assessing natural resources, and evaluating seismic hazards. Machine learning-based inversion algorithms have shown promising performance in regional (i.e., for exploration) and global velocity estimation, while their effectiveness hinges on access to large and diverse training datasets whose distributions generally cover the target solutions. Additionally, enhancing the precision and reliability of velocity estimation also requires incorporating prior information, e.g., geological classes, well logs, and subsurface structures, but current statistical or neural network-based methods are not flexible enough to handle such multi-modal information. To address both challenges, we propose to use conditional generative diffusion models for seismic velocity synthesis, in which we readily incorporate those priors. This approach enables the generation of seismic velocities that closely match the expected target distribution, offering datasets informed by both expert knowledge and measured data to support training for data-driven geophysical methods. We demonstrate the flexibility and effectiveness of our method through training diffusion models on the OpenFWI dataset under various conditions, including class labels, well logs, reflectivity images, and the combination of these priors. The performance of the approach under out-of-distribution conditions further underscores its generalization ability, showcasing its potential to provide tailored priors for velocity inverse problems and create specific training datasets for machine learning-based geophysical applications.