Efficient Learning of Stationary Diffusions with Stein-type Discrepancies

Fabian Bleile, Sarah Lumpp, Mathias Drton
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:1234-1242, 2026.

Abstract

Learning a stationary diffusion amounts to estimating the parameters of a stochastic differential equation whose stationary distribution matches a target distribution. We build on the recently introduced kernel deviation from stationarity (KDS), which enforces stationarity by evaluating expectations of the diffusion’s generator in a reproducing kernel Hilbert space. Leveraging the connection between KDS and Stein discrepancies, we introduce the Stein-type KDS (SKDS) as an alternative formulation. We prove that a vanishing SKDS guarantees alignment of the learned diffusion’s stationary distribution with the target. Furthermore, under broad parametrizations, SKDS is convex with an empirical version that is $\epsilon$-quasiconvex with high probability. Empirically, learning with SKDS attains comparable accuracy to KDS while substantially reducing computational cost, and yields improvements over the majority of competitive baselines.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-bleile26a, title = { Efficient Learning of Stationary Diffusions with Stein-type Discrepancies }, author = {Bleile, Fabian and Lumpp, Sarah and Drton, Mathias}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {1234--1242}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/bleile26a/bleile26a.pdf}, url = {https://proceedings.mlr.press/v300/bleile26a.html}, abstract = { Learning a stationary diffusion amounts to estimating the parameters of a stochastic differential equation whose stationary distribution matches a target distribution. We build on the recently introduced kernel deviation from stationarity (KDS), which enforces stationarity by evaluating expectations of the diffusion’s generator in a reproducing kernel Hilbert space. Leveraging the connection between KDS and Stein discrepancies, we introduce the Stein-type KDS (SKDS) as an alternative formulation. We prove that a vanishing SKDS guarantees alignment of the learned diffusion’s stationary distribution with the target. Furthermore, under broad parametrizations, SKDS is convex with an empirical version that is $\epsilon$-quasiconvex with high probability. Empirically, learning with SKDS attains comparable accuracy to KDS while substantially reducing computational cost, and yields improvements over the majority of competitive baselines. } }
Endnote
%0 Conference Paper %T Efficient Learning of Stationary Diffusions with Stein-type Discrepancies %A Fabian Bleile %A Sarah Lumpp %A Mathias Drton %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-bleile26a %I PMLR %P 1234--1242 %U https://proceedings.mlr.press/v300/bleile26a.html %V 300 %X Learning a stationary diffusion amounts to estimating the parameters of a stochastic differential equation whose stationary distribution matches a target distribution. We build on the recently introduced kernel deviation from stationarity (KDS), which enforces stationarity by evaluating expectations of the diffusion’s generator in a reproducing kernel Hilbert space. Leveraging the connection between KDS and Stein discrepancies, we introduce the Stein-type KDS (SKDS) as an alternative formulation. We prove that a vanishing SKDS guarantees alignment of the learned diffusion’s stationary distribution with the target. Furthermore, under broad parametrizations, SKDS is convex with an empirical version that is $\epsilon$-quasiconvex with high probability. Empirically, learning with SKDS attains comparable accuracy to KDS while substantially reducing computational cost, and yields improvements over the majority of competitive baselines.
APA
Bleile, F., Lumpp, S. & Drton, M.. (2026). Efficient Learning of Stationary Diffusions with Stein-type Discrepancies . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:1234-1242 Available from https://proceedings.mlr.press/v300/bleile26a.html.

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