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Life sciences · Preprint
arXiv · August 11, 2026
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This is an unpublished preprint describing a novel inverse sampling method for Lévy-driven generative models, addressing the challenge of nonlocal reverse processes via generator analysis and a decomposed sampler architecture. The work is theoretical and computational in nature, with validation limited to simulation of OFDM channel estimation under mixed noise; it has not undergone peer review and carries no direct clinical or established biomedical evidence.
Preprint. Intervention: Generator-guided inverse sampling algorithm for Lévy-driven generative models with decomposition into diffusion, small jump, and large jump components; neural network amortizes large jump rate activity..
Reversed jump component is governed by a state-dependent nonlocal density ratio Sampler decomposes dynamics into diffusion, small jump, and large jump components Neural network used only to amortize rate of large jump activities; jump amplitudes generated from analytically derived conditional distributions
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This is a methodological preprint presenting a novel computational framework for generative model sampling, not yet peer-reviewed, with validation limited to a single application domain (channel estimation) and no clinical or established biomedical outcomes.
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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.
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