{"ID":5937209,"CreatedAt":"2026-07-07T03:14:33.014478982Z","UpdatedAt":"2026-07-09T08:08:56.394513008Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.04780","arxiv_id":"2607.04780","title":"Non-Asymptotic Error Bounds for SMC with Biased Proposals: Application to Conditional Diffusion Sampling","abstract":"Sequential Monte Carlo (SMC) methods are a natural tool for post-hoc conditioning of pretrained generative models, but in many applications the mutation kernels used by the particle system are biased approximations of an ideal Feynman--Kac flow. This paper develops a non-asymptotic error analysis for such SMC samplers. Under forward-smoothing forgetting conditions, we decompose the total error into a kernel bias, measuring the effect of replacing the ideal transition kernels by approximate ones, and a finite-particle Monte Carlo error. Our approach relies on extending local Doeblin-type conditions and Lyapunov drift arguments for Markov kernels to conditional distributions, thereby enabling a principled control of the bias. We then instantiate this general framework for conditional sampling with score-based diffusion models, and derive the first non-asymptotic error bound that jointly controls initialization error, time discretization, and score approximation in the reverse diffusion dynamics as well as finite-particle Monte Carlo error.","short_abstract":"Sequential Monte Carlo (SMC) methods are a natural tool for post-hoc conditioning of pretrained generative models, but in many applications the mutation kernels used by the particle system are biased approximations of an ideal Feynman--Kac flow. This paper develops a non-asymptotic error analysis for such SMC samplers....","url_abs":"https://arxiv.org/abs/2607.04780","url_pdf":"https://arxiv.org/pdf/2607.04780v1","authors":"[\"Stanislas Strasman\",\"Gabriel Victorino Cardoso\",\"Sylvain Le Corff\",\"Vincent Lemaire\",\"Antonio Ocello\"]","published":"2026-07-06T08:10:13Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\"]","methods":"[\"Diffusion Model\"]","has_code":false}