Discrete Diffusion Inference-Time Control with Nested Sequential Monte Carlo

TL;DR - This paper introduces nested sequential Monte Carlo methods for steering discrete diffusion language models toward sequence-level rewards at inference time, without retraining. The methods address biases and sampling weaknesses in prior approaches and improve toxicity and fluency control in the reported experiments.

• Formulates nested SMC (NSMC) and fully adapted nested SMC (FA-NSMC) for Feynman–Kac steering.
• Identifies and corrects errors in earlier formulations that produce biased final estimates.
• Targets limitations of best-of-(n) sampling and bootstrap SMC, including overoptimism and weight degeneracy.
• NSMC and FA-NSMC consistently outperform both baselines on toxicity and fluency steering tasks.