# Probabilistic Inversion with Flow Matching

arXiv: https://arxiv.org/abs/2606.31288 · HTML: https://mlsanity.com/paper/2606.31288/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 9 of its 19 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## 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, 9 of 9)

- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Voicebox: Text-Guided Multilingual Universal Speech Generation at Scale](https://mlsanity.com/paper/2306.15687/) (2023)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [Guided Flows for Generative Modeling and Decision Making](https://mlsanity.com/paper/2311.13443/) (2023)
- [Fast Point Cloud Generation with Straight Flows](https://mlsanity.com/paper/2212.01747/) (2022)
- [Efficient Video Prediction via Sparsely Conditioned Flow Matching](https://mlsanity.com/paper/2211.14575/) (2022)
- [Wuerstchen: An Efficient Architecture for Large-Scale Text-to-Image Diffusion Models](https://mlsanity.com/paper/2306.00637/) (2023)

## Abstract (arXiv)

We demonstrate the application of Flow Matching, a technique originating from generative Artificial Intelligence, to probabilistic inversion in geophysical settings, such as seismic Full-Waveform inversion. We adapt the well-established mathematical theory of Flow Matching from generative Artificial Intelligence to the context of probabilistic inversion. We evaluate the approach with two case studies: a simple 2D velocity model to illustrate the general features of the method, and the OpenFWI dataset to show its capabilities for probabilistic inversion of more complex seismic velocity models.