# SAGE: Subsurface AI-driven Geostatistical Extraction with proxy posterior

arXiv: https://arxiv.org/abs/2604.00307 · HTML: https://mlsanity.com/paper/2604.00307/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 31 Mar 2026.

## Builds on (most cited first, 14 of 14)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Ambient Diffusion: Learning Clean Distributions from Corrupted Data](https://mlsanity.com/paper/2305.19256/) (2023)
- [Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Data](https://mlsanity.com/paper/2403.08728/) (2024)
- [Diffusion Models in Simulation-Based Inference: A Tutorial Review](https://mlsanity.com/paper/2512.20685/) (2025)
- [WISE: full-Waveform variational Inference via Subsurface Extensions](https://mlsanity.com/paper/2401.06230/) (2023)
- [An uncertainty-aware Digital Shadow for underground multimodal CO2 storage monitoring](https://mlsanity.com/paper/2410.01218/) (2024)
- [Self-Supervised Learning from Noisy and Incomplete Data](https://mlsanity.com/paper/2601.03244/) (2026)
- [Generative Geostatistical Modeling from Incomplete Well and Imaged Seismic Observations with Diffusion Models](https://mlsanity.com/paper/2406.05136/) (2024)
- [Machine learning-enabled velocity model building with uncertainty quantification](https://mlsanity.com/paper/2411.06651/) (2024)
- [Probabilistic Joint Recovery Method for CO2 Plume Monitoring](https://mlsanity.com/paper/2501.18761/) (2025)
- [Power-scaled Bayesian Inference with Score-based Generative Models](https://mlsanity.com/paper/2504.10807/) (2025)
- [A reduced-order derivative-informed neural operator for subsurface fluid-flow](https://mlsanity.com/paper/2509.13620/) (2025)

## Abstract (arXiv)

Recent advances in generative networks have enabled new approaches to subsurface velocity model synthesis, offering a compelling alternative to traditional methods such as Full Waveform Inversion. However, these approaches predominantly rely on the availability of large-scale datasets of high-quality, geologically realistic subsurface velocity models, which are often difficult to obtain in practice. We introduce SAGE, a novel framework for statistically consistent proxy velocity generation from incomplete observations, specifically sparse well logs and migrated seismic images. During training, SAGE learns a proxy posterior over velocity models conditioned on both modalities (wells and seismic); at inference, it produces full-resolution velocity fields conditioned solely on migrated images, with well information implicitly encoded in the learned distribution. This enables the generation of geologically plausible and statistically accurate velocity realizations. We validate SAGE on both synthetic and field datasets, demonstrating its ability to capture complex subsurface variability under limited observational constraints. Furthermore, samples drawn from the learned proxy distribution can be leveraged to train downstream networks, supporting inversion workflows. Overall, SAGE provides a scalable and data-efficient pathway toward learning geological proxy posterior for seismic imaging and inversion. Repo link: https://github.com/slimgroup/SAGE.