Posterior sampling in high-dimensional spaces using generative models holds significant promise for various applications, including but not limited to inverse problems and guided generation tasks. Despite many recent developments, generating diverse posterior samples remains a challenge, as existing methods require restarting the entire generative process for each new sample, making the procedure computationally expensive. In this work, we propose efficient posterior sampling by simulating Langevin dynamics in the noise space of a pre-trained generative model. By exploiting the mapping between the noise and data spaces which can be provided by distilled flows or consistency models, our method enables seamless exploration of the posterior without the need to re-run the full sampling chain, drastically reducing computational overhead. Theoretically, we prove a guarantee for the proposed noise-space Langevin dynamics to approximate the posterior, assuming that the generative model sufficiently approximates the prior distribution. Our framework is experimentally validated on image restoration tasks involving noisy linear and nonlinear forward operators applied to LSUN-Bedroom (256 x 256) and ImageNet (64 x 64) datasets. The results demonstrate that our approach generates high-fidelity samples with enhanced semantic diversity even under a limited number of function evaluations, offering superior efficiency and performance compared to existing diffusion-based posterior sampling techniques.

翻译：利用生成模型在高维空间中进行后验采样在反问题与引导生成等应用中具有重要前景。尽管近期取得诸多进展，生成多样化的后验样本仍面临挑战：现有方法需要为每个新样本重启完整生成过程，导致计算成本高昂。本研究提出通过在预训练生成模型的噪声空间中模拟朗之万动力学来实现高效后验采样。通过利用蒸馏流或一致性模型提供的噪声空间与数据空间映射关系，本方法能够无缝探索后验分布而无需重新运行完整采样链，显著降低计算开销。理论上，在生成模型充分逼近先验分布的假设下，我们证明了所提噪声空间朗之万动力学对后验分布的逼近保证。本框架在LSUN-Bedroom（256×256）和ImageNet（64×64）数据集上，针对含噪线性与非线性前向算子图像复原任务进行了实验验证。结果表明，即使在有限函数评估次数下，本方法仍能生成具有增强语义多样性的高保真样本，相比现有基于扩散的后验采样技术展现出更优的效率和性能。