# Non-Asymptotic Error Bounds for SMC with Biased Proposals: Application to Conditional Diffusion Sampling

arXiv: https://arxiv.org/abs/2607.04780 · HTML: https://mlsanity.com/paper/2607.04780/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 8 of its 47 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 8 of 8)

- [Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matching](https://mlsanity.com/paper/2504.11713/) (2025)
- [Reinforce Adjoint Matching: Scaling RL Post-Training of Diffusion and Flow-Matching Models](https://mlsanity.com/paper/2605.10759/) (2026)
- [Conditioning Diffusions Using Malliavin Calculus](https://mlsanity.com/paper/2504.03461/) (2025)
- [Non-Asymptotic Convergence of Discrete Diffusion Models: Masked and Random Walk dynamics](https://mlsanity.com/paper/2512.00580/) (2025)
- [Adjoint Matching through the Lens of the Stochastic Maximum Principle in Optimal Control](https://mlsanity.com/paper/2604.08580/) (2026)
- [Particle-Filtering-based Latent Diffusion for Inverse Problems](https://mlsanity.com/paper/2408.13868/) (2024)
- [On Forgetting and Stability of Score-based Generative models](https://mlsanity.com/paper/2601.21868/) (2026)
- [A unified perspective on fine-tuning and sampling with diffusion and flow models](https://mlsanity.com/paper/2605.00229/) (2026)

## Built on by (most cited first, 2 of 2)

- [A Stochastic Analysis Perspective on Diffusion Models](https://mlsanity.com/paper/2610.14133/) (2026)
- [Radial Tail Repair: Post-Training Correction for Diffusion and Flow Models](https://mlsanity.com/paper/2610.16851/) (2026)

## Abstract (arXiv)

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.