用新型核方法高效学习扩散模型，降低计算成本且保持精度。
Efficient Learning of Stationary Diffusions with Stein-type Discrepancies
- 引入斯坦因型核平稳性偏差（SKDS），通过核空间期望约束实现平稳分布匹配。
- 理论证明SKDS为零时可精确对齐目标分布，且在多数参数化下具凸性。
- 实测相比基线显著降耗提效，适合大规模扩散模型训练场景。
学习一个平稳扩散过程，即估计一个随机微分方程的参数，使其平稳分布与目标分布一致。本文基于近期提出的核平稳性偏差（KDS），该方法通过在再生核希尔伯特空间中评估扩散生成算子的期望来强制实现平稳性。借助KDS与斯坦因分歧之间的联系，我们提出一种替代形式——斯坦因型KDS（SKDS）。我们证明：当SKDS趋近于零时，可保证所学习扩散的平稳分布与目标分布完全对齐。此外，在广泛参数化条件下，SKDS具有凸性；其经验版本以高概率为ε-拟凸。实验表明，使用SKDS学习能获得与KDS相当的精度，同时大幅降低计算开销，并优于多数竞争基线。
原文摘要 · Abstract (English)
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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