用于Lévy驱动生成模型的生成器引导逆采样
Generator-Guided Inverse Sampling for Lévy-Driven Generative Models
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- University of Electronic Science and Technology of China（电子科技大学）
- Hong Kong University of Science and Technology（香港科技大学）
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中文总结 AI 辅助
本文针对Lévy驱动生成模型的非局域反向过程挑战，提出生成器引导的结构化逆采样器，将动力学分解为三类分量，结合神经网络与解析分布实现高效采样，在OFDM-SISO信道估计中表现出稳健性能与良好权衡。
中文摘要 AI 辅助
本文从马尔可夫生成器的角度研究Lévy驱动生成模型的逆采样。与传统扩散模型不同，Lévy驱动动力学涉及无限跳跃活动，这使得其反向过程具有非局域性，仅用得分信息难以表征。我们通过分析正向和反向生成器来应对这一挑战，推导得出反向跳跃分量通常成为由非局域密度比控制的、依赖状态的马尔可夫跳跃过程。这一观察结果启发了一种结构化反向采样器，其将动力学分解为扩散、小跳跃和大跳跃分量。基于此表征，我们针对一类具有对称α-稳定跳跃分量的各向同性线性Lévy SDE开发了计算上易处理的采样器。对于跳跃分量，神经网络仅用于摊销大跳跃活动的速率，而跳跃幅度则从解析推导的条件分布中生成，这提高了可解释性和可控性。在此设置下进一步引入高效实现技术，以避免昂贵的高维积分和采样。该采样器还被调整以近似观测引导采样，并应用于混合高斯和脉冲噪声下的OFDM-SISO信道估计。仿真显示出稳健的估计性能，且在复杂度与性能之间取得了良好的权衡。
英文摘要
This paper studies inverse sampling for Lévy-driven generative models from the perspective of Markov generators. Unlike conventional diffusion models, Lévy-driven dynamics involve infinite jump activities, which makes their reverse process nonlocal and difficult to characterize using score information alone. We address this challenge by analyzing the forward and reversed generators. It is derived that the reversed jump component generally becomes a state-dependent Markov jump process governed by a nonlocal density ratio. This observation motivates a structured reverse sampler that decomposes the dynamics into diffusion, small jump, and large jump components. Based on this characterization, we develop a computationally tractable sampler for a class of isotropic linear Lévy SDEs with symmetric $α$-stable jump components. For the jump component, the neural network is used only to amortize the rate of large jump activities, while jump amplitudes are generated from analytically derived conditional distributions, which improves interpretability and controllability. Efficient implementation techniques are further introduced under this setting to avoid expensive high-dimensional integration and sampling. The sampler is further adapted to approximate observation-guided sampling and applied to OFDM-SISO channel estimation under mixed Gaussian and impulsive noise. Simulations show robust estimation performance with a favorable tradeoff between complexity and performance.
