# Seismic Data Interpolation via Denoising Diffusion Implicit Models with Coherence-corrected Resampling

arXiv: https://arxiv.org/abs/2307.04226 · HTML: https://mlsanity.com/paper/2307.04226/

## Key facts

- Cited by 5 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 11 of its 55 references that are in the map.
- First posted on arXiv 9 Jul 2023.

## 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, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Towards Coherent Image Inpainting Using Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2304.03322/) (2023)
- [Deep Diffusion Models for Seismic Processing](https://mlsanity.com/paper/2207.10451/) (2022)
- [Seismic data interpolation based on U-net with texture loss](https://mlsanity.com/paper/1911.04092/) (2019)

## Built on by (most cited first, 5 of 5)

- [Controllable seismic velocity synthesis using generative diffusion models](https://mlsanity.com/paper/2402.06277/) (2024)
- [Condition Errors Refinement in Autoregressive Image Generation with Diffusion Loss](https://mlsanity.com/paper/2602.07022/) (2026)
- [A generative foundation model for an all-in-one seismic processing framework](https://mlsanity.com/paper/2502.01111/) (2025)
- [Vision-Driven Prompt Optimization for Large Language Models in Multimodal Generative Tasks](https://mlsanity.com/paper/2501.02527/) (2025)
- [SeisRDT: Latent Diffusion Model Based On Representation Learning For Seismic Data Interpolation And Reconstruction](https://mlsanity.com/paper/2503.21791/) (2025)

## Abstract (arXiv)

Accurate interpolation of seismic data is crucial for improving the quality of imaging and interpretation. In recent years, deep learning models such as U-Net and generative adversarial networks have been widely applied to seismic data interpolation. However, they often underperform when the training and test missing patterns do not match. To alleviate this issue, here we propose a novel framework that is built upon the multi-modal adaptable diffusion models. In the training phase, following the common wisdom, we use the denoising diffusion probabilistic model with a cosine noise schedule. This cosine global noise configuration improves the use of seismic data by reducing the involvement of excessive noise stages. In the inference phase, we introduce the denoising diffusion implicit model to reduce the number of sampling steps. Different from the conventional unconditional generation, we incorporate the known trace information into each reverse sampling step for achieving conditional interpolation. To enhance the coherence and continuity between the revealed traces and the missing traces, we further propose two strategies, including successive coherence correction and resampling. Coherence correction penalizes the mismatches in the revealed traces, while resampling conducts cyclic interpolation between adjacent reverse steps. Extensive experiments on synthetic and field seismic data validate our model's superiority and demonstrate its generalization capability to various missing patterns and different noise levels with just one training session. In addition, uncertainty quantification and ablation studies are also investigated.