提出高效近似后验采样方法，实现测量与先验的双重一致性。
Efficient Approximate Posterior Sampling with Annealed Langevin Monte Carlo
- 基于退火Langevin蒙特卡洛，构建可多项式时间采样的近似后验
- 在KL与Fisher散度上同时逼近真实后验与噪声先验后验
- 适用于图像超分辨率等任务，适合需快速生成高质量样本的场景
我们研究基于得分模型的后验采样问题。已知先验 $p(x)$ 的训练得分网络、观测模型 $p(y|x)$，目标是从后验 $p(x|y)$ 中采样。以往工作表明，在标准计算难解性假设下，该问题在KL散度意义下是不可 tractable（不可行）的。尽管如此，图像超分辨率、风格迁移和重建等任务中的主流算法仍表现出显著的实证成功。本文不依赖特定分布假设或受限设定，而是将此问题视为对分布进行“倾斜”以贴近观测信号的一般性问题。在最小假设下，我们证明可多项式时间地从一个分布中采样，该分布同时在KL散度上接近噪声先验的后验，在Fisher散度上接近真实后验。直观上，这种双重逼近确保了生成样本既符合观测又满足先验。据我们所知，这是首个关于（近似）后验采样在多项式时间内形式化成立的结果。
原文摘要 · Abstract (English)
We study the problem of posterior sampling in the context of score based generative models. We have a trained score network for a prior $p(x)$, a measurement model $p(y|x)$, and are tasked with sampling from the posterior $p(x|y)$. Prior work has shown this to be intractable in KL (in the worst case) under well-accepted computational hardness assumptions. Despite this, popular algorithms for tasks such as image super-resolution, stylization, and reconstruction enjoy empirical success. Rather than establishing distributional assumptions or restricted settings under which exact posterior sampling is tractable, we view this as a more general "tilting" problem of biasing a distribution towards a measurement. Under minimal assumptions, we show that one can tractably sample from a distribution that is simultaneously close to the posterior of a noised prior in KL divergence and the true posterior in Fisher divergence. Intuitively, this combination ensures that the resulting sample is consistent with both the measurement and the prior. To the best of our knowledge these are the first formal results for (approximate) posterior sampling in polynomial time.
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