# Direct Intermediate Initialization for Tilted Diffusion Samplers

arXiv: https://arxiv.org/abs/2610.06834 · HTML: https://mlsanity.com/paper/2610.06834/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 5 of its 23 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 5 of 5)

- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing](https://mlsanity.com/paper/2407.01521/) (2024)
- [Provable Diffusion Posterior Sampling for Bayesian Inversion](https://mlsanity.com/paper/2512.08022/) (2025)
- [Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priors](https://mlsanity.com/paper/2510.10968/) (2025)
- [Tempered Guided Diffusion](https://mlsanity.com/paper/2605.03712/) (2026)

## Abstract (arXiv)

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.