Multilevel and Sequential Monte Carlo for Training-Free Diffusion Guidance

TL;DR

A sequential Monte Carlo (SMC) framework is proposed that constructs an unbiased estimator of p_\theta(y|x_t) by integrating over the full denoising distribution via Monte Carlo approximation by integrating over the full denoising distribution via Monte Carlo approximation.

Abstract

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 constructs an unbiased estimator of $p_θ(y|x_t)$ by integrating over the full denoising distribution via Monte Carlo approximation. To ensure computational tractability, we incorporate variance-reduction schemes based on Multi-Level Monte Carlo (MLMC). Our approach achieves new state-of-the-art results for training-free guidance on CIFAR-10 class-conditional generation, achieving $95.6\%$ accuracy with $3\times$ lower cost-per-success than baselines. On ImageNet, our algorithm achieves $1.5\times$ cost-per-success advantage over existing methods.

Figures (6)

• Figure 1: Posterior distribution $p(x_0\mid x_t)$ for an 8-component ring GMM. Contours show $p(x_0 \mid x_t)$; $\times$ marks the noisy observation $x_t$; $\bullet$ shows the point estimate $\mathbb{E}[x_0\mid x_t]$; $\star$ indicates the true $x_0$. (a) At high noise ($t=900$), the posterior is multimodal and the point estimate lies in a low-density region at the center of the ring. (b) At moderate noise ($t=600$), the mass concentrates on two modes and the point estimate lies near the non-target mode.
• Figure 2: We perform six independent runs of label guidance for CIFAR-10. In a), no resampling occurs and ESS begins to collapse at $t=60.$ In b), resampling occurs at $\{70,60,50,40,30\}$. The relevant window remains stable across runs, suggesting it can be identified with a single exploratory run.
• Figure 3: Computation cost versus accuracy of SMC-MLMC as a function of the number of resampling steps compared to TFG-1 and TFG-4 tfg.
• Figure 4: Computation cost versus accuracy of SMC-MLMC as a function of number of particles $N$ for CIFAR-10.
• Figure 5: Qualitative comparison of CIFAR10 automobiles generated by (a) SMC-MLMC and (b) TFG-4 tfg.