Given an unconditional diffusion model $\pi(x, y)$, using it to perform conditional simulation $\pi(x \mid y)$ is still largely an open question and is typically achieved by learning conditional drifts to the denoising SDE after the fact. In this work, we express conditional simulation as an inference problem on an augmented space corresponding to a partial SDE bridge. This perspective allows us to implement efficient and principled particle Gibbs and pseudo-marginal samplers marginally targeting the conditional distribution $\pi(x \mid y)$. Contrary to existing methodology, our methods do not introduce any additional approximation to the unconditional diffusion model aside from the Monte Carlo error. We showcase the benefits and drawbacks of our approach on a series of synthetic and real data examples.

翻译：给定一个无条件扩散模型 $\pi(x, y)$，利用它来执行条件模拟 $\pi(x \mid y)$ 在很大程度上仍是一个开放性问题，通常需要通过事后学习去噪随机微分方程的条件漂移来实现。在本工作中，我们将条件模拟表述为对应于部分随机微分方程桥接的增广空间上的推断问题。这一视角使我们能够实现高效且原理性的粒子吉布斯采样器与伪边际采样器，其边际目标为条件分布 $\pi(x \mid y)$。与现有方法不同，除了蒙特卡洛误差外，我们的方法不会对无条件扩散模型引入任何额外的近似。我们通过一系列合成与真实数据示例展示了本方法的优势与局限。