Probabilistic Inversion with Flow Matching

Baldur Paulwitz; Stefan Buske

cs.LGJun 30, 2026

Probabilistic Inversion with Flow Matching

Authors: Baldur Paulwitz, Stefan Buske

Organizations: Institute of Geophysics and Geoinformatics, TU Bergakademie Freiberg

Abstract

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.

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Sep 14, 2026 · cs.CVJ/K move · Enter open · S save

Fast and Faithful: Principled Conditional Flow Matching for Inverse Problems

Shirin Shoushtari, Edward P. Chandler, Xiao Shi, Ulugbek S. Kamilov

Flow matching approaches to imaging inverse problems commonly incorporate measurements in two ways. Conditioning-based approaches supply measurement-derived information as a network input, often through concatenation, while inference-guided approaches combine an unconditional velocity field with a separate data-consistency update. In these common formulations, the forward model is not explicitly enforced within the learned conditional velocity field. We propose a principled parametrization of the measurement-conditional velocity field to solve inverse problems. Under linear interpolation, we express the conditional velocity

v(x_t,t,y)

in terms of the posterior mean

E[x_1 | x_t,y]

, and characterize that mean as the unique minimizer of a variational objective whose data-consistency term is explicit. We further prove that the velocity field defines a probability flow from the source distribution to the measurement-conditioned posterior. Splitting the variational objective yields a conditional velocity parameterization with operator-dependent data-consistency updates, which we train end-to-end under the flow-matching objective, with no additional guidance at inference. Our method achieves state-of-the-art PSNR with

50\times

fewer function evaluations than the strongest flow baseline. Varying the sampling steps provides test-time control over the distortion-perception trade-off without retraining.

Conditional Flow Matching Ill-Posed Inverse Problem Velocity Field Inverse Problem Variational Faithfulness

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Abstract

Explore similar work

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