Multilevel and Sequential Monte Carlo for Training-Free Diffusion Guidance

TL;DR

This paper introduces a training-free guidance method for diffusion models using a multilevel sequential Monte Carlo approach, improving accuracy and efficiency in class-conditional image generation.

Contribution

It develops an unbiased SMC framework with MLMC variance reduction for better guidance in diffusion models, surpassing existing methods in accuracy and cost-efficiency.

Findings

Achieves 95.6% accuracy on CIFAR-10 with lower computational cost.

Outperforms baselines in class-conditional ImageNet generation.

Provides unbiased posterior score estimation for diffusion models.

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 $p_\theta(y|x_t)$ 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.