Direct Intermediate Initialization for Tilted Diffusion Samplers
Direct intermediate initialization improves tilted diffusion SMC samplers on Gaussian-mixture inverse problems.
The paper pulls Gaussian-tilted intermediate targets used by diffusion posterior samplers back to weaker clean-space posteriors and maps samples with a Gaussian bridge. For the SMC sampler MCGDiff, the pulled-back observation variance is up to twice the diffusion-noise variance. Initializing at an intermediate time with moment-matching posterior sampling, then running only the remaining SMC suffix, improves sliced Wasserstein distance by roughly 2x on a structured Gaussian-mixture inverse problem and by more than an order of magnitude when the relevant mode is rare under the prior.
- MCGDiff is initialized at an intermediate time via a Gaussian bridge.
- Sliced Wasserstein improves about 2x at matched particle count.
- Rare-mode problems improve by more than an order of magnitude.
- Conditioning matters most when the mode is missing from the initial population.
From the original article
1 min read at arxiv.orgSome diffusion posterior samplers construct Gaussian-tilted intermediate distributions along the reverse process. We observe that these targets can be pulled back to clean-space posteriors with weaker conditioning, with samples transported analytically to the corresponding noisy-space target through a Gaussian bridge.
By Gregory D. Bellchambers · arxiv.org
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