Efficient Learning of Stationary Diffusions with Stein-type Discrepancies

Fabian Bleile; Sarah Lumpp; Mathias Drton

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arXiv · 2601.16597

Efficient Learning of Stationary Diffusions with Stein-type Discrepancies

Fabian Bleile·Sarah Lumpp·Mathias Drton

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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.

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Fabian Bleile, Sarah Lumpp, Mathias Drton. 2026-01-23. Efficient Learning of Stationary Diffusions with Stein-type Discrepancies. https://arxiv.org/abs/2601.16597

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