Theoretical Guarantees for SMC-Guided Diffusion Sampling
Abstract
Post-hoc conditioning of pretrained diffusion models can be addressed using Sequential Monte Carlo (SMC) methods. By evolving an interacting particle system, SMC-guided diffusion samplers combine unconditional reverse-diffusion dynamics with sequential reweighting to approximate conditional distributions. Nevertheless, even in the infinite-particle limit, the implemented sampler may differ from the ideal conditional target because of errors in the diffusion model, its numerical implementation, and the guidance mechanism. We characterize how these local errors propagate through forward-smoothing kernels, which jointly account for the reverse dynamics and the remaining conditioning information. This yields non-asymptotic error bounds that capture both finite-particle fluctuations and approximation errors arising from initialization, numerical integration, score approximation, and potential design. In doing so, we extend stability guarantees for diffusion models to the conditional setting. Finally, we apply our framework to several state-of-the-art SMC-guided diffusion algorithms, providing a unified theoretical perspective on their approximation mechanisms and sources of error.
Related
- Theoretical guarantees for stochastic gradient Langevin dynamics
- Path Invariance of a Quadrotor System under Cyber Attacks with Theoretical Guarantees
- Decentralized Safe Path Following for Multiple Quadrotors on Intersecting Paths with Theoretical Guarantees
- Differentially Private Distributed Optimization via the Intrinsic Randomness of Zeroth-Order Estimators: Sampling Geometry, Convergence, and Privacy Guarantees
- Recovery Guarantees for Posterior Sampling of One-Bit Compressed Sensing
BibTeX
@misc{strasman2026theoretical,
title = {{Theoretical Guarantees for SMC-Guided Diffusion Sampling}},
author = {Stanislas Strasman and Gabriel Victorino Cardoso and Sylvain Le Corff and Vincent Lemaire and Antonio Ocello},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.04780},
eprint = {2607.04780},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05679423v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Theoretical Guarantees for SMC-Guided Diffusion Sampling
AU - Stanislas Strasman
AU - Gabriel Victorino Cardoso
AU - Sylvain Le Corff
AU - Vincent Lemaire
AU - Antonio Ocello
PY - 2026
DA - 2026/09/28
PB - HAL
DO - 10.48550/arxiv.2607.04780
UR - https://hal.science/hal-05679423v2
AB - Post-hoc conditioning of pretrained diffusion models can be addressed using Sequential Monte Carlo (SMC) methods. By evolving an interacting particle system, SMC-guided diffusion samplers combine unconditional reverse-diffusion dynamics with sequential reweighting to approximate conditional distributions. Nevertheless, even in the infinite-particle limit, the implemented sampler may differ from the ideal conditional target because of errors in the diffusion model, its numerical implementation, and the guidance mechanism. We characterize how these local errors propagate through forward-smoothing kernels, which jointly account for the reverse dynamics and the remaining conditioning information. This yields non-asymptotic error bounds that capture both finite-particle fluctuations and approximation errors arising from initialization, numerical integration, score approximation, and potential design. In doing so, we extend stability guarantees for diffusion models to the conditional setting. Finally, we apply our framework to several state-of-the-art SMC-guided diffusion algorithms, providing a unified theoretical perspective on their approximation mechanisms and sources of error.
ER -