Semi-implicit distributions have shown great promise in variational inference and generative modeling. Hierarchical semi-implicit models, which stack multiple semi-implicit layers, enhance the expressiveness of semi-implicit distributions and can be used to accelerate diffusion models given pretrained score networks. However, their sequential training often suffers from slow convergence. In this paper, we introduce CoSIM, a continuous semi-implicit model that extends hierarchical semi-implicit models into a continuous framework. By incorporating a continuous transition kernel, CoSIM enables efficient, simulation-free training. Furthermore, we show that CoSIM achieves consistency with a carefully designed transition kernel, offering a novel approach for multistep distillation of generative models at the distributional level. Extensive experiments on image generation demonstrate that CoSIM performs on par or better than existing diffusion model acceleration methods, achieving superior performance on FD-DINOv2.

翻译：半隐式分布在变分推断与生成建模中展现出巨大潜力。分层半隐式模型通过堆叠多个半隐式层，增强了半隐式分布的表达能力，并可在给定预训练评分网络的条件下加速扩散模型。然而，其序列化训练常面临收敛缓慢的问题。本文提出CoSIM，一种连续半隐式模型，将分层半隐式模型扩展至连续框架。通过引入连续转移核，CoSIM实现了高效的无模拟训练。此外，我们证明CoSIM在精心设计的转移核下满足一致性条件，为生成模型在分布层面的多步蒸馏提供了新方法。在图像生成任务上的大量实验表明，CoSIM的性能与现有扩散模型加速方法相当或更优，在FD-DINOv2指标上取得了卓越表现。