# Stein Variational Gradient Descent

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arXiv Oct 14, 2026
Seismic velocity inversion drops its handcrafted prior: a diffusion model as projector cuts Marmousi MAE from 94.80 to 92.68
Full waveform inversion reconstructs subsurface velocity models from seismic records, but it is highly nonlinear and ill-posed, and an inaccurate initial model or noisy data can push it to a wrong solution. Bayesian full waveform inversion built on annealed Stein variational gradient descent previously constrained its particles with handcrafted Gaussian or smoothing priors that cannot represent complex geology. This work embeds a diffusion model trained on the GeoFWI dataset as an implicit geological projection operator inside the particle update, lowering mean absolute error on the Marmousi synthetic model from 94.80 with the classic method to 92.68, raising structural similarity from 0.69 to 0.72, and concentrating posterior uncertainty near deep structures and high-contrast interfaces.
Full waveform inversion reconstructs subsurface velocity models from seismic records, but it is highly nonlinear and ill-posed, and an inaccurate initial model or noisy data can push it to a wrong solution. Bayesian full waveform inversion built on annealed Stein variational gradient descent previously constrained its particles with handcrafted Gaussian or smoothing priors that cannot represent complex geology. This work embeds a diffusion model trained on the GeoFWI dataset as an implicit geological projection operator inside the particle update, lowering mean absolute error on the Marmousi synthetic model from 94.80 with the classic method to 92.68, raising structural similarity from 0.69 to 0.72, and concentrating posterior uncertainty near deep structures and high-contrast interfaces.
The University of Texas at Austin
Chao Li（First author）
Full Waveform Inversion Diffusion Model Stein Variational Gradient Descent Uncertainty Quantification
arXiv Oct 5, 2026
SCOUT transports generative behavioral priors toward high-value regions via test-time action refinement, achieving the best average performance on discrete and continuous offline MARL benchmarks
The work proposes SCOUT, an offline multi-agent reinforcement learning framework that separately trains a flow-matching behavioral prior and a decomposed value function, then at test time transports behavioral samples toward high-value regions via Stein variational gradient descent, using the number of transport steps in place of a fixed regularization coefficient; under the individual-global-max (IGM) principle it proves a single-term KL bound on the joint soft-value gap that vanishes as transport converges, with an irreducible additive residual proportional to the IGM violation; empirically it achieves the best average performance across discrete and continuous offline MARL benchmarks and yields improvements in all offline-to-online configurations.
The work proposes SCOUT, an offline multi-agent reinforcement learning framework that separately trains a flow-matching behavioral prior and a decomposed value function, then at test time transports behavioral samples toward high-value regions via Stein variational gradient descent, using the number of transport steps in place of a fixed regularization coefficient; under the individual-global-max (IGM) principle it proves a single-term KL bound on the joint soft-value gap that vanishes as transport converges, with an irreducible additive residual proportional to the IGM violation; empirically it achieves the best average performance across discrete and continuous offline MARL benchmarks and yields improvements in all offline-to-online configurations.
The University of Texas at Austin
Dongsu Lee（First author）
SCOUT Offline Multi-Agent Reinforcement Learning Test-Time Scaling Stein Variational Gradient Descent

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Seismic velocity inversion drops its handcrafted prior: a diffusion model as projector cuts Marmousi MAE from 94.80 to 92.68

SCOUT transports generative behavioral priors toward high-value regions via test-time action refinement, achieving the best average performance on discrete and continuous offline MARL benchmarks