New Sampling Method for L\'evy-Driven Generative Models

Generative models based on L\'evy processes, unlike standard diffusion models, involve infinite jump activities, making their reverse sampling process complex and difficult to characterize using only score information. This presents a significant challenge for generating high-quality samples. Researchers address this by analyzing the forward and reversed Markov generators, deriving that the reversed jump component becomes a state-dependent Markov jump process governed by a nonlocal density ratio. This insight leads to a structured reverse sampler that breaks down the dynamics into diffusion, small jump, and large jump components. The proposed method develops a computationally tractable sampler for specific L\'evy SDEs, using neural networks primarily to amortize large jump rates while deriving jump amplitudes analytically. This enhances interpretability and control. Efficient implementation techniques are also introduced to avoid costly high-dimensional integration. The sampler shows robust performance in applications like OFDM-SISO channel estimation under mixed noise.