Efficient Learning of Stationary Diffusions with Stein-type Discrepancies

• URL: http://arxiv.org/abs/2601.16597v2
• Date: Thu, 29 Jan 2026 13:58:58 GMT
• Title: Efficient Learning of Stationary Diffusions with Stein-type Discrepancies
• Authors: Fabian Bleile, Sarah Lumpp, Mathias Drton,
• Abstract summary: We build on the recently introduced kernel deviation from stationarity (KDS)<n>We introduce the Stein-type KDS (SKDS)<n>We prove that an alternative SKDS guarantees alignment of the learned diffusions stationary distribution with a target distribution.
• Score: 2.7528170226206448
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $ε$-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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