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.

Machine Learning (stat.ML); Machine Learning (cs.LG); Probability (math.PR)

arXiv:2607.04780 [stat.ML]

(or arXiv:2607.04780v2 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2607.04780 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.