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.

本研究解决了高维空间中使用生成模型进行后验采样的多样性不足问题。通过在预训练生成模型的噪声空间中模拟Langevin动态，我们提出了一种高效的后验采样方法，显著降低了计算开销。实验证明，该方法在图像修复任务上能生成高保真度的样本，表现出更好的效率和性能。 

基于生成先验的Langevin动态后验采样