Direct Intermediate Initialization for Tilted Diffusion Samplers
「直接中間初始化」技術：突破傾斜擴散採樣器的有限粒子瓶頸
Sequential Monte Carlo (SMC) diffusion samplers like MCGDiff struggle under finite particle budgets, often failing to capture rare posterior modes. This paper proposes Direct Intermediate Initialization (DII). By pulling back intermediate Gaussian-tilted targets to a softened clean-space posterior, samples can be generated via an approximate solver (like MMPS) at an intermediate timestep, then analytically mapped to the noisy target using a Gaussian bridge. Running only the remaining SMC suffix trades asymptotic consistency for performance, yielding a 2x improvement in sliced Wasserstein distance on Gaussian mixtures and over a 10x improvement on rare-mode inverse problems.
Key points
Pullback to Clean-Space Posterior
Pulls back intermediate Gaussian-tilted targets to clean-space posteriors with weaker conditioning, where the effective observation variance is up to twice the diffusion-noise variance.
Analytical Gaussian Bridge Mapping
Uses a Gaussian bridge to analytically transport samples from the softened clean-space posterior to the corresponding noisy-space target.
Hybrid Suffix Execution
Initializes directly at an intermediate timestep and runs only the remaining SMC suffix, trading asymptotic consistency for superior finite-particle performance.
Decisive for Rare-Mode Problems
Delivers over an order of magnitude improvement in rare-mode problems, where standard resampling fails to repopulate missing modes from the initial population.
How it works
Why it matters
Diffusion posterior sampling often suffers from mode collapse under finite particle budgets. By bypassing early diffusion steps using an analytical Gaussian bridge combined with an approximate solver, this work offers a highly practical hybrid framework. It significantly improves sample quality and mode coverage in complex inverse problems without requiring massive particle counts, facilitating more efficient Bayesian inference.
Who it affects
- AI Researcher
- AI Developer
How to use it
- 1High-accuracy posterior estimation in structured Gaussian-mixture inverse problems.
- 2Rare-mode posterior sampling to prevent mode collapse inherent in standard diffusion samplers.
Limitations & caveats
- The hybrid method sacrifices the sampler's asymptotic consistency to gain immediate finite-particle performance.
- It relies heavily on the quality of the approximate solver (e.g., MMPS) used to sample the softened clean-space posterior at initialization.
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