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 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.

Scalable Policy Maximization Under Network Interference

Many interventions, such as vaccines in clinical trials or coupons in online marketplaces, must be assigned sequentially without full knowledge of their effects. Multi-armed bandit algorithms have proven successful in such settings. However, standard independence assumptions fail when the treatment status of one individual impacts the outcomes of others, a phenomenon known as interference. We study optimal-policy learning under interference on a dynamic network. Existing approaches to this problem require repeated observations of the same fixed network and struggle to scale in sample size beyond as few as fifteen connected units -- both limit applications. We show that under common assumptions on the structure of interference, rewards become linear. This enables us to develop a scalable Thompson sampling algorithm that maximizes policy impact when a new $n$-node network is observed each round. We prove a Bayesian regret bound that is sublinear in $n$ and the number of rounds. Simulation experiments show that our algorithm learns quickly and outperforms existing methods. The results close a key scalability gap between causal inference methods for interference and practical bandit algorithms, enabling policy optimization in large-scale networked systems.