Multilevel and Sequential Monte Carlo for Training-Free Diffusion Guidance

We address the problem of accurate, training-free guidance for conditional generation in trained diffusion models. Existing methods typically rely on point-estimates to approximate the posterior score, often resulting in biased approximations that fail to capture multimodality inherent to the reverse process of diffusion models. We propose a sequential Monte Carlo (SMC) framework that integrates over the full denoising distribution to construct an unbiased Monte Carlo estimator of $p_{\theta }(y|x_t)$, avoiding the bias of existing training-free guidance methods. To ensure computational tractability, we incorporate variance-reduction schemes based on MultiLevel Monte Carlo (MLMC). We evaluate on three image generation tasks. On CIFAR-10 and ImageNet classifier guidance, our approach improves accuracy by 18 and 38 points respectively over the strongest training-free baseline. On CelebA-HQ joint-attribute guidance, three existing methods (DPS, LGD, TFG) used within our framework all outperform the closest SMC-based comparator (TDS) by 25-37 points, and improve over the strongest baseline by 2-14 points.