Direct Intermediate Initialization for Tilted Diffusion Samplers
Abstract
Some 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. For the sequential Monte Carlo (SMC) sampler MCGDiff, the effective observation variance of this pulled-back problem is up to twice the diffusion-noise variance. We exploit this structure to initialize MCGDiff directly at an intermediate time: an approximate solver samples the softened clean-space posterior, the Gaussian bridge maps these samples to the tilted target, and only the remaining SMC suffix is run. This trades asymptotic consistency for finite-particle performance. With moment-matching posterior sampling (MMPS) as the solver, the hybrid improves sliced Wasserstein distance by roughly 2× at matched particle count on a structured Gaussian-mixture inverse problem, and by more than an order of magnitude when the posterior-relevant mode is rare under the prior. A prior-initialization control, which retains the bridge but drops the clean-space conditioning, shows that on MCGDiff's standard Gaussian-mixture benchmark most of the improvement is insensitive to the conditioning. Conditioning the initialization gives a further consistent gain on the structured problem, and becomes decisive on a rare-mode problem, where resampling cannot repopulate a mode absent from the initial population.
Related
- Initialization-dependent BFGS trial rates for tilted absolute values
- A priori regularity of the reverse heat flow and dimension-dependent complexity of higher-order diffusion samplers
- Transformers as In-Context Samplers: From Closed-Form Diffusion to Estimation-Free Sampling
- Internal Guidance as a Sampling Method for Tilted Diffusion Models
- The Direct Scattering Transform for the Intermediate Long Wave Equation
BibTeX
@misc{bellchambers2026direct,
title = {{Direct Intermediate Initialization for Tilted Diffusion Samplers}},
author = {Gregory D. Bellchambers},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06834},
eprint = {2610.06834},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06834},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Direct Intermediate Initialization for Tilted Diffusion Samplers
AU - Gregory D. Bellchambers
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06834
UR - https://arxiv.org/abs/2610.06834
AB - Some 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. For the sequential Monte Carlo (SMC) sampler MCGDiff, the effective observation variance of this pulled-back problem is up to twice the diffusion-noise variance. We exploit this structure to initialize MCGDiff directly at an intermediate time: an approximate solver samples the softened clean-space posterior, the Gaussian bridge maps these samples to the tilted target, and only the remaining SMC suffix is run. This trades asymptotic consistency for finite-particle performance. With moment-matching posterior sampling (MMPS) as the solver, the hybrid improves sliced Wasserstein distance by roughly 2× at matched particle count on a structured Gaussian-mixture inverse problem, and by more than an order of magnitude when the posterior-relevant mode is rare under the prior. A prior-initialization control, which retains the bridge but drops the clean-space conditioning, shows that on MCGDiff's standard Gaussian-mixture benchmark most of the improvement is insensitive to the conditioning. Conditioning the initialization gives a further consistent gain on the structured problem, and becomes decisive on a rare-mode problem, where resampling cannot repopulate a mode absent from the initial population.
ER -