Initializing diffusion samplers at intermediate timesteps using pulled-back clean-space posteriors and Gaussian bridges can dramatically improve sample quality, especially when the posterior has modes that are rare under the prior.
This paper improves diffusion-based posterior sampling by initializing the sampler at an intermediate step rather than starting from pure noise. The key insight is that Gaussian-tilted targets along the reverse process can be reformulated as weaker clean-space posteriors, with samples transported analytically via a Gaussian bridge.